FINITE ELEMENT MODELING OF BLAST-INDUCED TRAUMATIC BRAIN INJURY

by

Chenzhi Wang

B.E., Nanjing University of Science and Technology, 2006

M.E., Nanjing University of Science and Technology, 2008

Submitted to the Graduate Faculty of

Swanson School of Engineering in partial fulfillment

of the requirements for the degree of

Doctor of Philosophy

University of Pittsburgh

2013

ii

UNIVERSITY OF PITTSBURGH

SWANSON SCHOOL OF ENGINEERING

This dissertation was presented

by

Chenzhi Wang

It was defended on

September 11th

, 2013

and approved by

Carey D. Balaban, PhD, Professor, Departments of Otolaryngology, Neurobiology,

Communication Science & Disorders, and Bioengineering

Mark C. Miller, PhD, Associate Research Professor, Department of Mechanical Engineering

& Materials Science

Xudong Zhang, PhD, Associate Professor, Department of Mechanical Engineering &

Materials Science

Dissertation Director: Jeffrey S. Vipperman, PhD, Associate Professor, Department of

Mechanical Engineering & Materials Science

iii

Copyright © by Chenzhi Wang

2013

iv

Human exposure to a blast wave itself without any fragment impact can still result in primary

blast-induced traumatic brain injury (bTBI). To investigate the mechanical response of human

brain to primary blast waves and to identify the injury mechanisms of bTBI, a three-dimensional

finite element head model consisting of the scalp, skull, cerebrospinal fluid, nasal cavity, and

brain was developed from the imaging data set of a human head. The finite element head model

was implemented with material models and was partially validated against a published cadaveric

experiment.

This study included three scenarios of blast-head interaction simulations using the same

five TNT doses: the simulations of head exposures to the blast waves coming from three

horizontal orientations (anterior, right lateral, posterior), to the blast waves generated from the

explosives laid on the ground, and to the blast waves within a small room. For the horizontal

blast-head simulations, the influences of the blast levels and exposure orientations on the

pressure and shear stress responses of brain were analyzed. For the simulation scenarios of the

ground blasts and the room blasts, the influences of the blast levels and the blast wave reflections

on the pressure and shear stress responses of brain were assessed. The patterns of intracranial

pressure waves and the high-pressure locations were investigated. Based on a published

pressure-based injury criterion of cerebral contusion, the locations and injury severities of

cerebral contusion for every simulation scenario were predicted. High von-Mises stresses were

FINITE ELEMENT MODELING OF BLAST-INDUCED TRAUMATIC BRAIN

INJURY

Chenzhi Wang, PhD

University of Pittsburgh, 2013

v

found on the cortex, brainstem, and spinal cord in every simulation. However, it was predicted

that diffuse axonal injury (DAI) did not occur in any simulation using a DAI criterion based on

von-Mises stress.

The mechanical properties of human bridging vein in an anisotropic, hyperelastic

constitutive model were obtained by fitting the data of an inflation test of a real human bridging

vein to the analytical equation of the inflation test. The obtained mechanical properties were

implemented in the finite element analysis of bridging vein rupture to predict the blast-induced

subdural hemorrhage by using the peak CSF pressures at the SSS of the anterior blast-head

simulations as the loading conditions.

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TABLE OF CONTENTS

TABLE OF CONTENTS ........................................................................................................... VI

LIST OF TABLES ................................................................................................................... VIII

LIST OF FIGURES .................................................................................................................... IX

PREFACE .................................................................................................................................. XII

1.0 INTRODUCTION ........................................................................................................ 1

1.1 MOTIVATION .................................................................................................... 1

1.2 BACKGROUND .................................................................................................. 4

1.3 LITERATURE REVIEW ON NUMERICAL SIMULATIONS OF TBI ...... 9

1.4 OVERVIEW OF RESEARCH PROCEDURES ............................................ 12

2.0 FINITE ELEMENT HEAD MODELING ............................................................... 15

2.1 HEAD GEOMETRIC MODELING AND FINITE ELEMENT

DISCRETIZATION ........................................................................................................... 16

2.2 MATERIAL MODELING OF HEAD............................................................. 24

2.3 VALIDATION OF FINITE ELEMENT HEAD MODEL ............................ 28

3.0 NUMERICAL IMPLEMENTATION OF SIMULATIONS OF BLAST-HEAD

INTERACTIONS ........................................................................................................................ 33

3.1 MATERIAL MODELS OF EXPLOSIVES AND AIR .................................. 33

3.2 NUMERICAL FORMULATIONS .................................................................. 35

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3.3 MODELING PROCEDURES OF BLAST-HEAD SIMULATION ............. 39

4.0 BLAST-HEAD INTERACTION SIMULATIONS OF HORIZONTAL

EXPOSURE TO BLAST ............................................................................................................ 45

4.1 PREPROCESSING OF SIMULATIONS ....................................................... 45

4.2 BRAIN PRESSURE RESPONSE TO HORIZONTAL BLAST ................... 49

4.3 BRAIN SHEAR STRESS RESPONSE TO HORIZONTAL BLAST .......... 64

5.0 BLAST-HEAD INTERACTION SIMULATIONS OF EXPOSURE TO

GROUND BLAST ....................................................................................................................... 70

5.1 PREPROCESSING OF SIMULATIONS ....................................................... 70

5.2 BRAIN PRESSURE RESPONSE TO GROUND BLAST ............................. 73

5.3 BRAIN SHEAR STRESS RESPONSE TO GROUND BLAST .................... 81

6.0 BLAST-HEAD INTERACTION SIMULATIONS OF EXPOSURE TO BLAST

IN A SMALL ROOM ................................................................................................................. 87

6.1 PREPROCESSING OF SIMULATIONS ....................................................... 87

6.2 BRAIN PRESSURE RESPONSE TO BLAST IN A SMALL ROOM ......... 90

6.3 BRAIN SHEAR STRESS RESPONSE TO BLAST IN A SMALL ROOM 99

7.0 FINITE ELEMENT ANALYSIS OF SUBDURAL HEMORRHAGE ............... 104

7.1 MECHANICAL TESTING OF HUMAN BRIDGING VEIN..................... 104

7.2 CONSTITUTIVE MODELING AND MATERIAL CURVE FITTING OF

BRIDGING VEIN ............................................................................................................ 107

7.3 INJURY PREDICTION OF SUBDURAL HEMORRHAGE ..................... 112

8.0 CONCLUSIONS AND DISCUSSIONS ................................................................. 116

BIBLIOGRAPHY ..................................................................................................................... 124

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LIST OF TABLES

Table 2-1. Number of every element type in each of the anatomical components of the FE human

head model .................................................................................................................................... 19

Table 2-2. Constitutive models and associated material parameters of FE human head model for

this study ....................................................................................................................................... 28

Table 3-1. Material parameters of TNT explosive........................................................................ 34

Table 4-1. Predicted contusion injury severities at typical cerebral sites with respect to impinging

BOPs at the blast incident side in the anterior blast-head simulations ......................................... 60

Table 4-2. Predicted contusion injury severities at typical cerebral sites with respect to impinging

BOPs at the blast incident side in the right lateral blast-head simulations ................................... 61

Table 4-3. Predicted contusion injury severities at typical cerebral sites with respect to impinging

BOPs at the blast incident side in the posterior blast-head simulations ....................................... 62

Table 5-1. Pressure ranges in kPa at various cerebral locations: No. 3 (cortex at SSS), No. 6

(frontal cortex), No. 11 (brain parenchyma), No. 14 (occipital cortex), No. 19 (lower brainstem),

No. 21 (hypothalamus), No. 22 (right temporal cortex) ............................................................... 78

Table 5-2. Peak von-Mises stresses in kPa at frontal cortex (gauge No. 6), occipital cortex (gauge

No. 14), right temporal cortex (No. 22) of the five simulations cases .......................................... 86

Table 6-1. Predicted contusion injury severities at typical cerebral sites with respect to impinging

BOPs at the blast incident side in the room blast-head simulations ............................................. 98

Table 7-1. Material parameters of human bridging vein ............................................................ 111

Table 7-2. Peak pressure tracked by the gauge No. 2 in the CSF at SSS, and the respective

maximum axial Cauchy stress and failure prediction of the BV with respect to the impinging

BOP at the blast incident side ..................................................................................................... 115

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LIST OF FIGURES

Figure 1-1. Ideal Friedlander wave (Bauman et al. 2009) .............................................................. 5

Figure 1-2. The most common cerebral locations of contusion (blue) and subdural hemorrhage

(purple) (Taber et al. 2006) ............................................................................................................. 6

Figure 1-3. Human cerebral bridging veins in the superior sagittal sinus (SSS) on a lateral view

of a cadaver (Han et al. 2007) ......................................................................................................... 6

Figure 2-1. The three-dimensional finite element model of scalp: (a) Overall view, (b) Sagittal

cross-sectional view showing the internal details ......................................................................... 20

Figure 2-2. The three-dimensional finite element model of skull: (a) Overall view, (b) Transverse

cross-sectional view showing the internal details ......................................................................... 21

Figure 2-3. Three-dimensional finite element models of CSF and nasal cavity ........................... 22

Figure 2-4. Three-dimensional finite element model of brain: (a) Overall view of brain model,

(b) Bottom view showing the cerebrum, cerebellum, brainstem, and spinal cord ........................ 23

Figure 2-5. Validation of the FE head model by applying the measured input force of Nahum's

experiment..................................................................................................................................... 30

Figure 2-6. Comparison between the pressure-time histories of simulation and Nahum's

cadaveric test at (a) Frontal cortex and (b) Posterior fossa ........................................................... 32

Figure 3-1. (a) 2D 450g TNT air-blast model was remapped into the Euler-FCT grid of the air

space model in order to form (b) the complete 3D blast-head model of 450g TNT ..................... 43

Figure 3-2. Locations of gauges: (a) Sagittal cross-sectional view, (b) Transverse cross-sectional

view ............................................................................................................................................... 44

Figure 4-1. (a) The five surfaces of the air space were assigned with the open boundary condition

indicated by orange color, (b) The FE head model was exposed to the blasts from the anterior,

posterior, and right lateral horizontal orientations ........................................................................ 48

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Figure 4-2. Blast wave propagating through the head during the first 0.5 ms of the 250g TNT

blast-head simulation of the anterior blast scenario: (a) 0.2 ms, (b) 0.4 ms, (c) 0.5 ms, (d) 0.75 ms

....................................................................................................................................................... 50

Figure 4-3. Pressure-time histories recorded by various gauge points for the anterior blast-head

simulations: (a) No. 24 in atmosphere (b) No. 2 in the CSF at SSS, (c) No. 6 on the frontal

cortex, (d) No. 14 in the occipital cortex, (e) No. 18 at the posterior margin of the tentorium

cerebelli, (f) No. 19 on the lower brainstem ................................................................................. 52

Figure 4-4. Pressure distributions of the brain in the 400g TNT blast-head simulations of all blast

orientations .................................................................................................................................... 56

Figure 4-5. Predicted contusion injury location and severity of the anterior blast-head simulations

....................................................................................................................................................... 60

Figure 4-6. Predicted contusion injury location and severity of the right lateral blast-head

simulations .................................................................................................................................... 61

Figure 4-7. Predicted contusion injury location and severity of the posterior blast-head

simulations .................................................................................................................................... 62

Figure 4-8. von-Mises stress time histories of the gauge points No. 6 (frontal cortex), No. 14

(occipital cortex), No. 22 (right temporal cortex), and No. 23 (left temporal cortex) in the 450g

TNT blast-head simulation cases: (a) Anterior blast orientation, (b) Right lateral blast orientation,

(c) Posterior blast orientation ........................................................................................................ 67

Figure 4-9. von-Mises stress time-histories of gauge No. 19 at lower brainstem and the

associated von-Mises stress distributions showing peak von-Mises stresses in the 450g TNT

blast-head simulation cases: left - anterior orientation (2.45 ms), middle - right lateral orientation

(1.85 ms), right - posterior orientation (3.43 ms) ......................................................................... 68

Figure 5-1. Ground blast exposure simulation scenario: (a) 3D view, (b) Y-Z plane view ......... 72

Figure 5-2. Blast wave propagating during the first 1.2 ms of the 250g TNT ground blast-head

simulation ...................................................................................................................................... 74

Figure 5-3. Pressure distributions of the brain in the 250g TNT ground blast-head simulation

from 1.3 ms to 1.8 ms ................................................................................................................... 75

Figure 5-4. Pressure-time histories recorded by various gauge points of the five ground blast-

head simulations: (a) No. 24 in atmosphere (b) No. 2 in the CSF at SSS, (c) No. 6 on the frontal

cortex, (d) No. 14 on the occipital cortex, (e) No. 19 on the lower brainstem, (f) No. 21 on the

hypothalamus ................................................................................................................................ 77

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Figure 5-5. Distributions of von-Mises stress of the brain were shown in the sagittal cross-

sectional view for the 250g TNT ground blast-head simulation at different times from 1.6 ms to

2.1 ms ............................................................................................................................................ 82

Figure 5-6. The time histories of von-Mises stress recorded by various gauge points of the five

ground blast-head simulations: (a) No. 3 on cortex at SSS, (b) No. 6 on the frontal cortex, (c) No.

14 on the occipital cortex, (d) No. 19 on the lower brainstem, (e) No. 21 on the hypothalamus, (f)

No. 22 on the right temporal cortex .............................................................................................. 83

Figure 6-1. Computational schematic of 3D air blast within the small room which was assigned

with open boundary condition (B.C.) at the anterior surface ........................................................ 89

Figure 6-2. Time-lapse contours of a blast wave propagating within the room at 2.0 ms, 3.0 ms,

4.0 ms, 4.5 ms, 5.0 ms and at 8.0 ms for the 250g TNT room blast-head simulation .................. 91

Figure 6-3. Atmospheric pressure time histories tracked by (a) the air gauge point No. 24 in the

frontal space of the head model, (b) the air gauge point No. 25 in the rear space of the head

model............................................................................................................................................. 92

Figure 6-4. Pressure-time histories recorded by various gauge points for the room blast-head

simulations: (a) No. 2 in CSF at SSS, (b) No. 6 in the frontal cortex, (c) No. 14 in the occipital

cortex, (d) No. 18 at the posterior margin of the tentorium cerebelli, (e) No. 19 on the lower

brainstem, (f) No. 22 on the right temporal cortex ....................................................................... 95

Figure 6-5. Pressure distributions of the brain in the 400g TNT room blast-head simulation from

4.5 ms to 5.0 ms ............................................................................................................................ 96

Figure 6-6. Predicted contusion injury location and severity of the room blast-head simulations98

Figure 6-7. Distributions of von-Mises stress in the sagittal cross-sectional view of the brain for

the 400g TNT room blast-head simulation at different times from 4.5 ms to 5.0 ms ................ 100

Figure 6-8. The time histories of von-Mises stress recorded by various gauge points for the room

blast-head simulations with five amounts of TNT: (a) No. 3 on cortex at SSS, (b) No. 6 on the

frontal cortex, (c) No. 14 on the occipital cortex, (d) No. 19 on the lower brainstem, (e) No. 21

on the hypothalamus, (f) No. 22 on the right temporal cortex .................................................... 102

Figure 7-1. Human bridging vein mounted in the inflation-extension vascular testing system

(Wang et al. 2012)....................................................................................................................... 106

Figure 7-2. Experimental data and analytical solution from fitted material parameters ............ 111

Figure 7-3. Axial Cauchy stress of the bridging vein finite element analysis corresponding to

impinging BOP at the blast incident side: (a) 291 kPa, (b) 321 kPa, (c) 349 kPa, (d) 379 kPa, (e)

413 kPa........................................................................................................................................ 114

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PREFACE

I would like to thank my advisor, Dr. Jeffrey S. Vipperman, sincerely for his guidance and

supervision. His profound knowledge, patient guidance, and constant encouragement were the

biggest driving forces to make this dissertation appear. I would like to thank Dr. Carey D.

Balaban for his research suggestions, providing the bridging vein samples, and for teaching me

the anatomy of human head and the pathology of blast-induced traumatic brain injury. I sincerely

thank Dr. Jae Bum Pahk and Adam R. Wood for their collaborations on the 3D modeling of

human head. I would express my appreciation to Dr. Mark C. Miller for his help on revising the

research proposal which was eventually granted by NSF to support me. I thank Dr. David A.

Vorp and Joseph E. Pichamuthu for their help on the experiments of human bridging veins.

I thank Dr. Xudong Zhang, Dr. Mark C. Miller, and Dr. Carey D. Balaban for serving on

my dissertation committee and their invaluable comments.

I thank Dr. Kai Liu, Ms. Yali Yang, and all my friends who help me during my living in

Pittsburgh.

My deeply thanks to my wife Weiwei Jiao, my father Shaoqing Wang, my mother

Shuling Qiu, my father in law Jie Jiao, and my mother in law Chunling Wang, for their love,

understanding, help, and encouragement.

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1.0 INTRODUCTION

1.1 MOTIVATION

The number of civilians and army personnel diagnosed with blast-induced traumatic brain injury

(bTBI) has increased significantly due to the growing use of the improvised explosive devices

(IEDs) in the current conflicts and terrorist activities at Iraq and Afghanistan. Improvement in

protection devices and medical treatment has also contributed to the lowest mortality of the

people who experienced blast assaults. IED detonation can produce primary blast wave and high-

velocity fragments. The brain injury resulting from the primary blast waves, the impacts of blast-

propelled fragments, the collisions between blast-propelled people and stagnant object are

categorized to primary, secondary, and tertiary bTBI, respectively.

The clinical observations have leaded to the hypothesis that bTBI is a stress wave

dominated phenomenon as opposed to impact/acceleration/deceleration-induced brain injury,

typically encountered in automobile and sports accidents (DePalma et al. 2005, Taber et al.

2006). Cerebral contusion, subdural hematoma (SDH), and diffuse axonal injury (DAI) are the

major injury types of bTBI (Taber et al. 2006, Kocsis and Tessler 2009). The challenge in

determining the mechanism of primary bTBI comes from the difficulties in measuring the injury

process of bTBI in vivo and from the difficulty of distinguishing the blast wave dominated brain

injury from other types of injuries in the chaotic environment of the battlefield. Rigorous

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epidemiological studies are not available so far. Cerebral contusion and diffuse cerebral edema

have been reported in the clinical cases of primary bTBI detected by CT or MRI (Benzinger et al.

2009). Case reports have shown intracranial hemorrhage including subdural hematoma happened

following IED blast and industrial explosion accident (Murthy et al. 1979, Ling et al. 2009).

However clinical studies are not able to fully explain the precise neuropathology of primary

bTBI. So far, much of what we know about bTBI was determined from animal studies (Bauman

et al. 2009, Long et al. 2009, Cheng et al. 2010). These studies have helped researchers better

understand the pathology of bTBI, but the findings still have not explained well the detailed

mechanisms of bTBI. Moreover, the results of animal studies are not able to parametrically

interpret the injury mechanism of human bTBI due to the geometrical differences. However, the

development of protection device and medical treatment requires a clear understanding of the

injury mechanisms of bTBI. In biomechanical engineering, finite element (FE) modeling and

simulation, serving as an alternative to experiment, is able to help understand the biomechanical

details and to increase research efficiency.

The primary goal of this study is to understand the biomechanical mechanisms of blast-

induced traumatic brain injury using finite element modeling and simulation. Three FE

simulation scenarios of blast waves and head interactions including the horizontal blast-head

interaction simulations, the ground blast-head interaction simulations, and the room blast-head

interaction simulations were taken in this dissertation with the motivation to investigate the

mechanism, injury occurrence possibility, and potential injury severity of cerebral contusion,

diffuse axonal injury, and subdural hematoma (bSDH). The horizontal blast-head interaction

simulations reproduced the human brain exposures to blast waves from the anterior, right lateral,

and posterior orientations, and were motivated to evaluate the sensitivity of brain responses to

3

various pathways of blast waves. The simulations of human head exposures to the blast waves

generated near the ground were developed with the motivation to evaluate the brain response of a

standing person to a blast wave generated by an IED and to predict whether ground blasts with

the same explosive charges as the horizontal blast-head simulations could lead to more severe

brain injuries. The simulations of human head exposures to the blast waves loaded in a room

were built in order to evaluate the effects of the wall reflections of blast waves on the cerebral

mechanical responses. The obtained intracranial pressures and von-Mises stresses can help to

understand the biomechanical behaviors of brain subjected to blast waves and the brain

sensitivities to various blast factors.

There is currently a lack of fundamental understanding in the literature about the

mechanism of blast-induced human bridging vein rupture. In order to study the blast-induced

subdural hemorrhage, known to be caused by bridging vein rupture, an experimental approach on

a human bridging vein segment was taken in this dissertation to calibrate the mechanical

properties of bridging vein by measuring the intraluminal pressure and diameter of the bridging

vein under the internal fluid inflation. The material parameters related to an anisotropic

hyperelastic constitutive model were calculated by using a nonlinear regression method which

fitted the results of bridging vein inflation experiment to the constitutive model. The injury

severities of subdural hemorrhage in the anterior blast-head simulations, which were concluded

as the most injurious case, were evaluated by implementing the calculated material parameters to

the finite element analysis of bridging vein rupture.

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1.2 BACKGROUND

Blast-induced traumatic brain Injury (bTBI), called as the signature injury of the wars in Iraq and

Afghanistan (Elder and Cristian 2009), is more prevalent nowadays due to the intensive use of

improvised explosive devices (IED). Some recent reports estimated that a significant number of

service members had been affected by TBI, for example, the study of RAND company estimated

320,000 TBIs from a total number of 1.64 million US Armed forces deployed since 9/11

(Tanielian and Jaycox 2008). Mild TBI constituted 10-20% of the cases of those service

members diagnosed as TBI positive (Moore et al. 2009). Unlike previous wars, improved

battlefield medical care and improved body armor significantly reduced the mortality rate of the

service members who experienced blasts (Chen and Huang 2011). However, the soldiers

survived the exposures to blasts are suffering blast-induced traumatic brain injury (bTBI). The

primary bTBI is the cerebral lesion caused by the direct effects of the blast-generated blast waves

propagating through the head.

When an explosion occurs, ambient pressure rises sharply and forms a blast wave, a

shock front of high atmospheric pressure (positive impulse) higher than the standard atmospheric

pressure. As the initial overpressure wave dissipates, ambient pressure plummets, causing a

negative pressure impulse that is lower than the ambient pressure (Taber et al. 2006). This

negative impulse in atmosphere attracts the air from the areas of normal pressure, therefore

causes a reversed blast wind toward the low pressure area. The pressure-time history of blast

wave is described by the ideal Friedlander wave which has positive phase and negative phase

(Figure 1-1).

It is believed that over-pressurization waves cause hemorrhages and diffuse neuronal

damage throughout the brain, therefore inducing neurological dysfunction (Taber et al. 2006,

5

Kocsis and Tessler 2009). Headache, hearing impairment, and balance dysfunction are the major

symptoms of mild TBI that occur acutely after exposure to low level blasts. Mild TBI impedes

its sufferers returning to normal activities, and can persist chronically (Hoge et al. 2008 , Terrio

et al. 2009, Hoffer et al. 2010, Hoffer et al. 2013). Blast over-pressurization waves

instantaneously increase pressure in body tissues, forming pressure waves traveling in the

intracranial tissues. Once the resultant stresses in the intracranial tissues exceed the tolerable

threshold, traumatic brain injury occurs.

Figure 1-1. Ideal Friedlander wave (Bauman et al. 2009)

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Figure 1-2. The most common cerebral locations of contusion (blue) and subdural hemorrhage (purple) (Taber et al.

2006)

Figure 1-3. Human cerebral bridging veins in the superior sagittal sinus (SSS) on a lateral view of a cadaver (Han et

al. 2007)

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Although the pathophysiology of blast-related TBI is very complicated and has not been

fully understood, it is thought that the rapid ambient pressure changes lead to traumas such as

concussion, subdural hematoma (SDH), and diffuse axonal injury (DAI) (Taber et al. 2006,

Kocsis and Tessler 2009). Figure 1-2 shows that contusion has the most common locations at the

inferior, lateral, and anterior cortex of the frontal and temporal lobes, and that subdural

hemorrhage commonly occurs at the frontal and parietal convexities (Taber et al. 2006). The

subdural space contents appear to be particularly vulnerable to over-pressurization damage.

Subdural hemorrhage, known as the bleeding between the dura matter and the arachnoid matter,

is caused by the rupture of bridging veins (Figure 1-3) which cross the subdural space. Diffuse

axonal injury is a type of shear-induced injury, resulting from the disruption of axons and small

vessels. The cortico-medullary (gray matter-white matter junctions) is particular vulnerable to

the shearing and stretching forces (Taber et al. 2006).

The experimental studies of both large and small animals provide important data to help

identify the pathophysiological characteristics of bTBI. Several animal studies found evidence

supporting that cerebral contusion, diffuse axonal injury, and subdural hematoma/hemorrhage

are the major pathophysilogical characteristics of bTBI. Most of large-animal models of blast

injury utilized chemical explosives as the source of blast wave (Saljo et al. 2008, Bauman et al.

2009), while the majority of small-animal studies (Long et al. 2009, Rafaels et al. 2011,

Sundaramurthy et al. 2012) utilized compressed air-driven shock tubes to produce shock waves.

In the study of Saljo et al. (2008), pigs were exposed to the controlled blasts which

simulated real battlefield blast scenarios such as the explosions generated by howitzer, bazooka,

automatic rifle in free field, the explosions in an enclosure, and underwater blasts. The rats were

exposed to blast waves generated by a shock tube. Pressure-time histories recorded by the gauges

8

within the pig brains in the howitzer experiments were found to have a strong similarity with

those in air. Macroscopic examinations revealed that subdural hemorrhages were observed in

21% of the animals exposed to the automatic rifle in free field and in 7% of those exposed to the

bazooka. Histological examination of porcine brains also revealed that small parenchymal and

subarachnoid hemorrhages predominated in the occipital lobe, cerebellum, and medulla

oblongta/lower brainstem.

Bauman et al. (2009) used a bi-directionally open-ended blast tube, a surrogate of a

HUMVEE crew-compartment, a building consisted of four walls without roof, to perform blast

experiments on swines. The blast tube included the heavy-walled driver chamber where the

chemical explosives were immobilized, the expansion cone, and the test section in which swine

was restrained to sustain blasts from different distances. The angiography data reported by the

blast-tube experiment indicated that the emergence of vasospasm was one salient

pathophysiological characteristic of exposure to explosion.

Long et al. (2009) studied the striking neuro-pathological changes of rat brains exposed

to the 126 and 147 kPa air blasts by using a shock tube. Rats exposed to the 147 kPa air blast had

prominent areas of cortical cell loss, gliosis, and infiltration, along with extensive fiber

degeneration shown by histological studies of rat brain slices. The rat brains in the 126 kPa air

blast did not show any cell loss despite extensive fiber degeneration.

Cheng et al. (2010) developed a unique blast on rat model to simulate the blast effects on

brain. An electric detonator with the equivalent of 400 mg TNT was developed as the explosive

source while the rat was fixed in the specially designed cabin in which the restricted rat brain

could only be exposed to the blast wave. Capillary damage, enlarged intercellular and vascular

9

space in the cortex, diffuse subarachnoid hemorrhage, edema, and degeneration of nerve fibers

were observed.

Rafaels et al. (2011) exposed twelve male New Zealand white rabbits whose bodies were

protected by test fixtures to shock waves. Histological evaluation revealed subdural and

subarachnoid hemorrhages in the nonresponsive respiratory-arrested specimens. Cerebral

contusion, subdural hemorrhage, and subarachnoid hemorrhage occurred together in all non-

surviving specimens. Injury risk was evaluated by scaling techniques on the blast over-pressure

and duration combinations.

Sundaramurthy et al. (2012) examined the role of animal placement location along the

length of the shock tube in which rats were placed to measure the surface and intracranial

pressures. In addition, they developed an anatomically accurate rat head model to simulate blast

effects on rats under the same experimental conditions.

1.3 LITERATURE REVIEW ON NUMERICAL SIMULATIONS OF TBI

A number of finite element head models have been created by researchers to study bTBI. Taylor

and Ford (2009) developed a finite element head model consisting of skull, white matter, gray

matter, CSF and air in sinuses by segmenting a data set of high resolution photographic images.

The direct exposure of this head model to a blast wave of 1.3 MPa peak pressure from anterior,

posterior, and lateral directions were simulated for 2 ms, showing focal areas of elevated

pressure, volumetric tension, and deviatoric stress in the brain. The authors concluded that

multifocal axonal injury might happen due to stress localization initially before the onset of any

linear or angular acceleration. Chafi et al. (2009) simulated the blast loadings of three different

10

TNT amounts on a finite element head model comprised of brain, falx and tentorium, CSF, dura

matter, pia matter, skull bone, and scalp for up to 5 ms, and predicted significant positive and

negative pressures alternating at the coup and contrecoup sites. They assessed the possibility of

bTBI using three different injury predictors based on intracranial pressure (ICP), shear stress,

and principal strain. Moore et al. (2009) used an numerical head model which is based on MRI

images for three simulations of a 5.2 atmosphere pressure blast, an 18.6 atmospheric pressure

blast, and a 5m/s impact on a head. The highest pressures and stresses experienced were located

at the right temporal region, for which the blast wave was incident. The results suggested that the

blast effects on the head of a 50% lethal dose of blast lung injury were comparable to the

concussive impact injury. Grujicic et al. (2010) developed a finite element head model

assembled with a helmet to study the mitigation effect of the advanced combat helmet against

blast. By comparing the simulation results using the helmet protected head and unprotected head,

it was concluded that the current combat helmet did provide some level of protection against

mild bTBI. By using the same finite element head model, Grujicic and his colleagues also

studied the effects of using polyurea as the helmet pad material to protect human heads from

blast (Grujicic et al. 2010). Nyein et al. (2010) developed a FE head model based on the

geometric segmentation of MRI images, and studied the intracranial pressure and von-Mises

stresses of the head under three conditions: unprotected head, head protected by a helmet, and

the head protected by both helmet and face shield. Head exposure to an anterior blast wave with

an incident overpressure of 10 atm was simulated for each of the conditions. It was suggested

that the existing combat helmet did not significantly mitigate blast harmfulness, but did not

worsen it either. In contrast, the harmfulness of blast wave was reduced by combinative use of

the helmet and face shield. Ganpule et al. (2012) simulated the blast wave-head interactions as

11

the blast wave traversed the finite element head model consisting of the skin, skull,

subarachnoidal space, and brain. They also built a shock tube to test the surface effects of blast

wave impinging on a dummy head. The measured surface pressure of the dummy head model

was used to validate their numerical simulations. It was concluded that the “coup and

contrecoup” injury patterns encountered in impact TBI also occurred in their blast-head

simulations.

There also had been a long history of finite element modeling of human head to study

impact-induced TBI before the computational studies of bTBI sprung up recently. Ruan (1994)

built a FE head model using pure hexahedral elements and investigated the model sensitivities to

various material models and to various loading characteristics of impacts. Zhang et al. (2001)

investigated the human brain responses to the frontal and lateral impacts to study the directional

sensitivity by using a partially validated three-dimensional finite element head model

(WSUBIM) with various anatomic structures. Later on, combining the results of finite element

studies and actual field accident data, Zhang et al. (2004) derived the injury threshold of impact-

induced cerebral contusion based on the predicted intracranial pressures using a pressure-based

contusion criterion (Ward et al. 1980). Zhang et al. (2004) also derived the injury threshold of

diffuse axonal injury based on von-Mises shear stress in the midbrain of the brainstem. Kleiven

(2006) investigated the brain responses to impacts of different directions and durations by using

an experimentally validated finite element head model comprised of the scalp, skull, brain,

meninges, CSF, and simplified models of eleven pairs of parasagittal bridging veins. Sayed et al.

(2008) studied diffuse axonal injury and brain cavitation due to impact using a partially validated

finite element human head model. A novel constitutive model capable of capturing the cerebral

damage mechanisms was developed for the head modeling. Although the injury mechanism of

12

impact TBI is distinct from that of bTBI, the mechanical properties used in the computational

studies of impact TBI were often used by the computational studies of bTBI (Chafi et al. 2009,

Moss et al. 2009, Taylor and Ford 2009, Ganpule et al. 2012).

1.4 OVERVIEW OF RESEARCH PROCEDURES

The primary objective for this research is to find out the injury severity of the blast-induced

traumatic brain injury under the blast loadings from various blast scenarios of five different

explosive charges using the methods of finite element modeling and simulation.

In the first stage of this study, an anatomically correct human head model was generated

from the segmentation of a high resolution MRI data set of a real human head. The head model

was constituted by five major anatomical structures: scalp, skull, nasal cavity, cerebrospinal

fluid, and brain matter. The segmented 3D head model was meshed by the Lagrangian meshing

algorithm as volume meshes. State of art constitutive relations were adopted for the material

modeling of the FE head model. In order to verify the accuracy of FE head model, the FE head

model was numerically validated against the frontal cadaveric impact experiment of Nahum et al.

(1977). The loading and boundary conditions of the head model in the validation simulation were

applied according to the protocol of the cadaveric experiment. The frontal pressure-time history

in the validation simulation was compared with that measured at the same gauge location in the

Nahum's cadaveric experiment to evaluate the predictive accuracy of the FE head model.

After the FE head model was numerically validated, the FE head model was immersed

into the numerical air space model for the further simulations of blast wave loading on the head.

The air space model was developed as a 3m by 1.8m by 3m cuboid volume which was

13

discretized as an Eulerian region in order to allow the numerical treatment of the formation and

propagation of primary blast waves. The air space model was assigned with the material

properties of ideal air which were described by the equation of state. Three scenarios of blast-

head interaction simulations involving the horizontal blast-head scenario, the ground blast-head

scenario, and the room blast-head scenario using the 250g, 300g, 450g, 400g, and 450g TNT

charges. The finite element simulations of blast-head simulations were solved using the

commercial explicit finite element package ANSYS AUTODYN® (ANSYS 2012) with its

embedded Euler-Lagrangian coupling method for the fluid-structure interaction (FSI). For each

TNT weight, the three horizontal blast-head simulation sets and the room blast-head simulation

scenario predicted the same impinging blast overpressure (BOP) at the blast incident side. The

pressure time histories and von-Mises stress time histories at various intracranial locations were

tracked for the simulations in each blast-head simulation scenario. The patterns of pressure

distributions and von-Mises stress distributions in the brain were studied. The sensitivities of

brain mechanical responses to the blast factors including the blast intensities, blast orientations,

blast wave reflections by the ground and room walls were investigated. How the predicted

intracranial pressures and von-Mises stresses were related to the blast waves was discussed for

each blast-head simulation scenario. The predicted intracranial pressures and von-Mises stresses

at several cerebral locations helped to evaluate the occurrences and severities of cerebral

contusion and diffuse axonal injury based on the published injury criterions. The predicted injury

severities of contusions at various cerebral locations in the horizontal blast-head simulations and

the room blast-head simulations were related to the predicted impinging BOPs at the proximal

side to blast. The relative skull and brain motion was predicted to be nearly zero in every blast-

head simulation. The peak positive pressures in the CSF at the superior sagittal sinus (SSS) were

14

speculated to be the main mechanical causation of the bridging vein rupture which led the

subdural hematoma. The anterior blast-head simulations and the ground blast-head simulations

had the most injurious cases of subdural hemorrhage. In addition, they have the same values of

peak positive pressures in the CSF at the SSS, therefore, the finite element analyses of subdural

hemorrhage were only based on the results of the anterior blast-head simulations.

Due to the fact that there was no reported experimental data on human cerebral bridging

veins to derive the accurate material properties, vascular inflation experiments were conducted in

this study on a human bridging vein sample to obtain the data of the relationship between the

inflating pressure and the vascular outer diameter. This experimental data was essential for the

calculations of the material parameters in a selected anisotropic constitutive model, known as the

Holzapfel-Gasser-Ogden model (Holzapfel et al. 2000), in order to numerically model the

nonlinear mechanical behavior of human bridging veins. The material parameters of human

bridging vein were calculated by fitting the experimental results to the Holzapfel-Gasser-Ogden

model using the nonlinear regression analysis.

A series of separate finite element analyses of bridging vein rupture for the anterior blast-

head simulations, concluded to be the most injurious cases, were carried out using an

axisymmetric finite element bridging vein model assigned with the calculated material

parameters. The predicted maximum axial Cauchy stresses of bridging vein were compared with

the yielding criterion of bridging vein to forecast the injury occurrence of the blast-induced

subdural hemorrhage.

15

2.0 FINITE ELEMENT HEAD MODELING

This chapter describes the details of the geometric development of the 3D head model, the

procedure of finite element discretization of the head geometric model, and the constitutive

modeling of each of the anatomical components of the FE head model. One of the main efforts to

build the FE head model was the development of the three-dimensional geometric model

reflecting the real anatomy of human head. The three dimensional geometry was created from

the two-dimensional magnetic resonance imaging (MRI) files of a real human head. Once the

geometry of a human head was established, it was imported into the finite element meshing tool

ANSYS ICEM-CFD

(ANSYS 2012) to be spatially discretized into a finite element grid.

Before using the FE head model for the blast simulations, it is essential to clarify the numerical

accuracy of the FE head model which was constituted by the finite element grid and the material

models. Although the cadaveric experiments of blast TBI are not reported so far in academia,

there is a widely recognized cadaveric human head impact test which provides bTBI researchers

valuable data to evaluate their numerical head models (Nahum et al. 1977). The mechanical

process involved in the impact on the structure is similar to that which exists in the blast loading

on structure - both of them can be categorized as nonlinear transient dynamic processes, so once

the FE head model is validated by this impact experimental data, some confidence can be

assumed for the simulation of the blast-head interaction. Therefore, a FE impact analysis of the

MRI based anatomically correct human head model is carried out by comparing the pressure

16

response of the FE head model and its counterpart in the experimental results under the same

impact loading conditions as the experiment (Nahum et al. 1977).

2.1 HEAD GEOMETRIC MODELING AND FINITE ELEMENT DISCRETIZATION

The three-dimensional geometric model of a human head was developed from a set of two-

dimensional MRI images of an actual human head. Reconstructing a three dimensional

geometric model of human head from MRI data has become the widely recognized method to

capture the detailed anatomical features of the complex geometry of the human head for the

computational studies of bTBI (Chafi et al. 2009, Moore et al. 2009, Taylor and Ford 2009,

Grujicic et al. 2010, Ganpule et al. 2012). Some of them include more cerebral parts (Chafi et al.

2009, Moore et al. 2009, Grujicic et al. 2010), than others (Taylor and Ford 2009, Ganpule et al.

2012). The FE head model built by Chafi et al. (2009) from CT data included scalp, skull, CSF,

and brain meshed by solid elements, as well as dura, falx, tentorium, and pia meshed by shell

elements. The FE head model built by Moore et al. (2009) segmented eleven distinct anatomical

structures including skin/fat, skull, ventricle, glia, white matter, gray matter, eyes, venous sinus,

CSF, air sinus, and muscle from MRI. Grujicic et al. (2010) purchased a CAD head model of six

distinct sections including brain, CSF, small brain, brainstem, pituitary gland, and skull. Taylor

and Ford (2009) constructed a FE head model based on the segmentation of MRI to represent

skull, white matter, gray matter, and CSF. The FE head model constructed by Ganpule et al.

(2012) included skin, skull, brain, and subarachnoid space.

The MRI data for this study were obtained from the International Consortium for Brain

Mapping database (ICBM 2011). The head modeling was based on the same MR images used in

17

the previous studies (Wang et al. 2011, Wang et al. 2012), while it was improved by segmenting

more structural details for this study. The MRI data of a female head consisted of 176 T1-

weighted slices of 2562 pixels taken at 1 mm intervals. In order to form the anatomically correct

three-dimensional solid model of a human head, each image slice of the MRI data was

segmented into five different anatomical components: (1) scalp, (2) skull, (3) cerebrospinal fluid

(CSF), (4) nasal cavity, and (5) brain. BrainSuite software was employed for the first stage of the

segmentation (BrainSuite 2011), i.e. to initially segment the MRI data into four different

anatomical masks including scalp, skull, CSF, and brain. A mask was referred to the surface or

contour representation of an anatomical component. The advantage of using the BrainSuite

software was that its automatic segmentation tool can automatically segment a human head MRI

into scalp, skull, CSF, brain. The automatic segmentation was not only very efficient compared

to the manual user segmentation, it was also accurate in segmenting the geometrical detail of the

brain gyri. However, the accuracy of the anatomical masks obtained in this stage was not perfect.

For example, the nasal cavity was geometrically segmented together with the CSF in the

automatic segmentation. Therefore, the second stage of the segmentation task was to correct the

inaccurate geometric representations produced in the first stage.

During the second stage, the masks created in BrainSuite were output as IMG files which

were imported into the MIMICS

13.0 software (Materialise 2011) for further editing. MIMICS

software is a powerful medical image (for CT, MRI, microCT, CBCT, Ultrasound, Confocal

Microscopy) processing tool capable of segmentation, three-dimensional modeling, and FEA

meshing. In MIMICS

, the mask of the nasal cavity was segmented from the CSF as an

independent anatomical component; the skull layer between the nasal cavity and the CSF was

also segmented; the inaccurate geometrical representation at the vertebrae was corrected. During

18

the third stage, the five masks were used to create the three-dimensional non-manifold assembly

which assembled a three-dimensional representation of the human head geometric model in

MIMICS

. Finally, the three-dimensional model of the human head was output in the form of a

Stereolithography file (STL), which can be input into a finite element meshing tool. Due to the

resolution of the MRI data, some essential simplifications were adopted in the geometric

modeling. The skin, muscle, fat, and any other tissues covering the skull model were modeled

together as the whole scalp model. The dura mater, a semi-rigid layer firmly attached to the

skull, was modeled together with the skull because it was too thin to be distinguished from the

skull. CSF, a natural fluid shock-absorber protecting brain, separates the brain from the skull and

enables the relative motion between skull and brain. In this study, the whole CSF model

integrated all the cerebrospinal fluid, sinuses, ventricles, and any other tissues in the space

between the skull model and the brain model. The cerebrum, cerebellum, brainstem, and spinal

cord were modeled together as the whole brain model.

In the present study, the three-dimensional geometric model of human head in STL

format was imported and meshed by the mesh generation software ANSYS ICEM CFD

, which

allowed users to produce high-quality volume meshes or surface meshes. Due to some of the

very complex geometrical areas of the brain model and the CSF model, such as the gyri, a pure

hexahedral mesh could not be achieved in the present study. The three-dimensional geometric

model of human head was automatically meshed into a mixture of linear hexahedral elements,

pentahedral elements, and tetrahedral elements. For each component, a core region of large

volume was filled by hexahedral elements, which have a more robust performance than

pentahedral elements and tetrahedral elements. The pentahedral elements and tetrahedral

elements have a better geometric adaptability than hexahedral elements, and thus were used to

19

mesh the very complex regions which could not be meshed by hexahedral elements. The whole

scalp model contained 280,175 elements (Figure 2-1). The eyes were covered for the sake of

anonymity. The whole skull model contained 154,658 elements (Figure 2-2). The CSF was

meshed into 54,878 elements. The nasal cavity, completely enveloped by skull, was meshed into

12,024 elements. The three dimensional FE models of the CSF and nasal cavity are shown in

Figure 2-3. The models of the cerebrum, cerebellum, brainstem and spinal cord were also

modeled together to constitute the whole brain model consisting of 105,575 elements (Figure

2-4). The whole FE human head model consisted of 607,310 elements. The element types and

the respective element numbers for each anatomical component can be found in Table 2-1.

The final FE head model was imported into the explicit nonlinear FE software ANSYS

AUTODYN

for the assignment of material models, and subsequent blast-head interaction

simulations.

Table 2-1. Number of every element type in each of the anatomical components of the FE human head model

Element Type Number of finite elements

Scalp Skull CSF Nasal Cavity Brain

Hexahedron 6782 164 21 179 12758

Pentahedron 7340 518 84 316 4652

Tetrahedron 266053 153976 54773 11529 88165

20

(a)

(b)

Figure 2-1. The three-dimensional finite element model of scalp: (a) Overall view, (b) Sagittal cross-sectional view

showing the internal details

21

(a)

(b)

Figure 2-2. The three-dimensional finite element model of skull: (a) Overall view, (b) Transverse cross-sectional

view showing the internal details

22

Figure 2-3. Three-dimensional finite element models of CSF and nasal cavity

23

(a)

(b)

Figure 2-4. Three-dimensional finite element model of brain: (a) Overall view of brain model, (b) Bottom view

showing the cerebrum, cerebellum, brainstem, and spinal cord

24

2.2 MATERIAL MODELING OF HEAD

The constitutive models and their associative material parameters of the five anatomical

constituents of the head model were adopted from the literature. The constitutive relation of

scalp and nasal cavity was linear elastic and was described by the bulk modulus and shear

modulus, representing dilatational/volumetric and deviatoric/shear responses respectively. The

dilatational behavior described only by bulk modulus has the form of a linear equation of state in

AUTODYN

:

(2.1)

where P is the hydrostatic pressure, K is bulk modulus, and is the compression. The

material constants of the scalp and the nasal cavity were chosen from the bTBI study of Moore et

al. (2009). Bulk modulus K, density ρ, and shear modulus G of the scalp were 34.7 MPa, 1.04 g/

cm3, and 5.88 MPa respectively. The bulk modulus K and shear modulus G of the scalp in this

study were also identical to the corresponding values calculated by K = E/3(1-2) and G =

E/2(1+) using the Young's modulus E and Poisson's ratio of scalp/skin in other literatures

(Zhang et al. 2001, Chafi et al. 2009, Ganpule et al. 2012). Most of the computational studies of

bTBI did not include the model of nasal cavity (Chafi et al. 2009, Moss et al. 2009, Taylor and

Ford 2009, Panzer et al. 2012), while some of the literature just modeled the nasal cavity

together with skull (Grujicic et al. 2010), or with the subarachnoid space (Ganpule et al. 2012). It

was found that only Moore et al. (2009) included the air sinus in their FE head model, so bulk

modulus, density, and shear modulus of the nasal cavity in the present study were 2.19 GPa, 1.04

g/cm3, and 225.3 Pa, respectively, picked from the study by Moore et al. (2009).

25

Skull is composed of bone material, and it has the highest rigidity among all the

anatomical parts of the head. In order to capture the large volumetric compressions of the skull

that may arise in the severe blast events with high overpressures, the dilatational part of the skull

constitutive model was represented by the Mie-Gruneisen equation of state (EOS), which is also

known as the "shock-Hugoniot" EOS, and is expressed by:

( )

[ ( )]

(2.2)

(2.3)

In equation (2.2), P is pressure, ρ is the density; in equation (2.3), Us is the shock

velocity, UP is the particle velocity. The reference density 0, sound speed C0 and s are the

material parameters. For the modeling of skull, the reference density was 0 = 1.412 g/cm3, the

parameter C0 was 1,850 m/s, and the dimensionless parameter s was 0.94. Similar to the scalp

and the nasal cavity, the deviatoric response of the skull was only described by a single material

parameter, the shear modulus G, calculated as 2.664 GPa by the corresponding Young's modulus

E and Poisson's ratio from literature. Since Grujicic et al. (2010) picked the material

parameters of skull from the study of Moore et al. (2009), all the material parameters of the skull

for the present study can be viewed as identical to those in the study of Moore et al. (2009).

Hence, the complete mechanical properties of the skull model were characterized by the

combination of the Mie-Gruneisen equation of state (EOS) and shear modulus, describing the

dilatational and deviatoric responses respectively.

CSF is known as a Newtonian fluid that fills the subarachnoid space and ventricular

system. The mechanical properties of CSF were recognized to be very close to that of water

since the density and viscosity of CSF are very similar to that of water (Zhang et al. 2001). Some

26

of the simulation studies of bTBI used a linear elastic model for the dilatational part of the

constitutive model of CSF (Chafi et al. 2009, Taylor and Ford 2009, Ganpule et al. 2012), they

used the value 0.5 or 0.49 for the Poisson's ratio of CSF to describe the CSF as an

incompressible solid. Moore et al. (2009) used the Tait EOS for the modeling of CSF. However,

The Tait EOS was not supported by AUTODYN

14.0. Panzer et al. (2012) used the Mie-

Gruneisen EOS for the CSF and assigned it to have the material constants of water. In the present

study, the volumetric/hydrostatic properties of the CSF model were characterized by equation

(2.2) and equation (2.3) (Mie-Gruneisen/Hugoniot equation of state). The material parameters C0

(1,647 m/s), 0 (0.998 g/cm3), s (1.921) for the CSF model were chosen to have the

corresponding properties of water from the published engineering standards (Cooper 1996).

Since tetrahedral elements and pentahedral elements in the finite element CSF model were only

supported by Lagrangian formulations in AUTODYN

14.0, a very low shear modulus of 500 Pa

was assigned to the CSF model to accommodate the hydrostatic property, following what Zhang

et al. (2001) did for the material modeling of the CSF shear property.

The cerebrum, cerebellum, brainstem, and spinal cord mainly consist of white and gray

matter. The material properties of white and gray matters are different, but both exhibit complex

mechanical properties including structural anisotropy and viscoelasticity. White matter is mainly

composed of axonal fibers with various directions, therefore exhibiting regional difference of

mechanical behavior. Gray matter is mainly composed of cell bodies of neurons, and can be

viewed as isotropic. Much research efforts have been put by academia into developing state of

art constitutive models of brain matter in order to better numerically model the mechanical

behavior of brain (Miller 1999, Ning et al. 2006, Shen et al. 2006, Prevost et al. 2011). In the

present study, a linear elastic model for dilatational response and a linear viscoelastic constitutive

27

law for deviatoric response were adopted for the whole brain model. The constitutive relations

and the associated material constants of brain were derived by Zhang et al. (2001) based an in

vitro vibration tests of human brain tissue (Shuck and Advani 1972). In addition, Zhang et al.

(2001) validated their finite element head model by simulating the same impact on their head

model against the impact test conducted by Nahum et al. (1977) on a cadaver human head. The

volumetric property of brain tissue was characterized by bulk modulus only. The deviatoric

property of brain tissue was described by a generalized three-term Maxwell viscoelastic model

which expresses the shear modulus by:

( ) ( ) (2.4)

where G0 is the short-term shear modulus, G∞ is the long-term shear modulus, β is the

viscous decay constant, and t is time. The properties of white matter and gray matter reported by

Zhang et al. (2001) were different. But in our study, we did not separate white matter and gray

matter in the stage of geometrical modeling. Since white matter accounts for a higher portion of

brain than gray matter, in the present study, the material parameters of the whole brain were

assigned as those of the white matter reported by Zhang et al. (2001). So, G0 was 41 KPa, G∞

was 7.8 KPa, and β was 700 s-1

for the shear properties of the brain model. The density ρ and

bulk modulus K of the brain model were assigned by 1.04 g/cm3 and 2.19 GPa respectively. The

constitutive models and the associated material parameters used for the finite element head

model in this study were summarized in Table 2-2.

28

Table 2-2. Constitutive models and associated material parameters of FE human head model for this study

Part Constitutive model Material Parameters

Scalp Linear Elastic K = 34.7 MPa, G = 5.88 MPa, ρ = 1.04g/ cm3

Nasal cavity Linear Elastic K = 2.19 GPa, G = 225.3 Pa, ρ = 1.04g/ cm3

Skull Mie-Gruneisen EOS C0 = 1,850 m/s, s = 0.94, 0 = 1.412 g/cm3

G = 2.664 GPa

CSF Mie-Gruneisen EOS C0 = 1,647 m/s, s = 1.921, 0 = 0.998 g/cm3

G = 500 Pa

Brain Viscoelastic K = 2.19 GPa, ρ = 1.04g/ cm3

G0 = 41 KPa, G∞ = 7.8 KPa, β = 700 s-1

2.3 VALIDATION OF FINITE ELEMENT HEAD MODEL

The anatomically fidelic human FE head model generated from the MRI data set was validated

using the experimental data of a published experiment of frontal impact on a cadaveric head

(Nahum et al. 1977). A large number of researchers validated their finite element head models

using this published data of the cadaveric test for their computational studies of impact TBI

(Ruan and Prasad 1995, Willinger et al. 1999, Zhang et al. 2001, Horgan and Gilchrist 2003,

Kleiven 2006, Elsayed et al. 2008, Chen and Ostoja-Starzewski 2010, Sporns et al. 2012).

Ganpule et al. (2012) validated their FE head model using the published data of the cadaveric

impact experiments previously mentioned (Nahum et al. 1977), indicating a good match between

the result of the head impact simulation and that of the experiment although the head model of

29

Ganpule et al. (2012) only had four anatomical parts. This indicated that the number of the

individual anatomical structures in the head model does not play a significant role in the

numerical accuracy of head model as long as the major structures have been created.

This cadaveric experiment has been widely recognized by TBI researchers as a standard

to validate their FE head models. In this experiment, the foreheads of seated stationary human

cadavers were impacted by a rigid mass moving at a constant velocity along the anterior-

posterior direction in the mid-sagittal plane. The heads were rotated forward in order to incline

the Frankfort anatomical plane 45o to the horizontal plane. Several padding materials were

placed in between the skull and rigid mass to adjust the duration of the loading forces. The input

force on the skull was measured during the impact test. The intracranial pressure-time histories at

several cerebral locations were recorded by transducers. Only the figures of the pressure-time

history and the input force-time history of the experiment No. 37 were reported. Therefore we

only referred to the No. 37 experiment in this report as the Nahum's experiment in the following

content.

In order to simulate Nahum's experiment, the measured input force of this test was

applied to the center area of the forehead of head model in the anterior-posterior direction with

45o inclined to the horizontal as a form of a distributed load, as shown in Figure 2-5.

30

Figure 2-5. Validation of the FE head model by applying the measured input force of Nahum's experiment

31

The pressure-time histories were recorded at the same frontal cortex and the posterior

fossa areas as in the Nahum's experiment during the simulation of the FE head model validation.

The comparison between the simulated profile and the experimental profile for each of the two

areas shows good agreement (Figure 2-6). The frontal peak pressure of the validation simulation

was almost the same as that of the Nahum's experiment, while the peak negative pressure at

posterior fossa of the simulation was 7.74 % less than that of the cadaveric experiment. So, the

present FE head model was considered basically accurate to be used as the blast-head

simulations. Since the FE head model was not validated against any cadaveric head experiments

under blast loadings, it currently can only be claimed as partially validated. Once a valid blast-

cadaveric head experiment is performed, it would be used to fully validate the current FE head

model.

32

(a)

(b)

Figure 2-6. Comparison between the pressure-time histories of simulation and Nahum's cadaveric test at (a) Frontal

cortex and (b) Posterior fossa

33

3.0 NUMERICAL IMPLEMENTATION OF SIMULATIONS OF BLAST-HEAD

INTERACTIONS

This chapter examines the modeling and simulation methods of TNT air blasts using Euler

formulations. The governing equations of shock wave generation and propagation, along with the

material models of explosives and air are explained. Numerical techniques in AUTODYN

for

solving the governing equations and the associated constitutive models of air blast are

introduced. It also explained how the Euler-Lagrange coupling algorithm was applied to solve

the fluid-structure interaction (FSI) problem involved in the blast-head simulations.

3.1 MATERIAL MODELS OF EXPLOSIVES AND AIR

The material model used for the detonation modeling in the present study was the so called

Jones-Wilkins-Lee (JWL) equation of state (Lee et al. 1968), which is suitable for hydrodynamic

computations of a wide range of explosive expansions. The JWL EOS is able to model most

types of high explosives with the form stated as

(

) (

)

(3.1)

where P is the pressure, V is the relative volume. A, B, R1, R2, and ω are all material

constants determined from the experiments of the explosive materials, such as TNT and PETN.

34

The material parameters of TNT used in this study are listed in Table 3-1 based on literature (Lee

et al. 1973).

Table 3-1. Material parameters of TNT explosive

Density

(g/cm3)

Detonation

velocity (m/s)

Energy/unit

volume

(kJ/m3)

C-J

pressure

(GPa)

A

(GPa)

B

(GPa)

R1 R2 ω

1.63 6930 6.0e6 21 373.77 3.75 4.15 0.9 0.35

The constitutive property of air was represented by an equation of state for an ideal gas:

( )

(3.2)

where P is the current absolute pressure in air, E is the initial internal volumetric energy

density, and ρ is the current mass density. ρ0 is the initial mass density of the ideal gas

(0.001225g/cm3 for air). As the adiabatic exponent, γ has the value 1.4 for air. It can be shown

that if the expansion ratios are very large, the first and second terms on the right side of the JWL

equation tend to negligible and therefore making the behavior of explosive approaches that of an

ideal gas. At large expansion ratios, where the explosive has expanded by a factor of

approximately 10 from its original volume, ANSYS AUTODYN

14.0 automatically switches

from the JWL to the ideal gas law, and thus avoid potential numerical difficulties.

35

3.2 NUMERICAL FORMULATIONS

The numerical formulations adopted in this study are identical to those used in the previous

studies (Wang et al. 2011, Wang et al. 2012). Explosives generate a very rapid release of energy

in the order of microseconds when subjected to suitable stimuli. In the theory of blast mechanics,

a detonation is assumed to be a shock wave which propagates through the unreacted explosive

material instantaneously releasing energy and converting the explosive into blast products

(AUTODYN 2003). The Rankine-Hugoniot relations, representing the conservation of mass,

momentum and energy across the front of shock wave, are used to describe the shock wave

generation and propagation in explosives across the reaction zone, and to describe the shock

wave traveling in ordinary media. For detonation in explosives, the Rankine-Hugoniot relations

for the unreacted explosive and the detonation products are expressed as:

( ) ( )⁄ (3.3)

( )( ) (3.4)

( )( ) (3.5)

In equations (3.3), (3.4), and (3.5), v0, p0, e0, Q are the specific volume, pressure, specific

internal energy, and the specific chemical energy of the unreacted explosive, respectively. In the

detonation products, u is the particle velocity, D is the detonation velocity, v, p, e are the specific

volume, pressure, and specific internal energy, respectively. The equation (3.3) and equation

(3.5) are known as the Rayleigh line, and the Hugoniot curve.

In order to relate the state variables before and behind the shock front in ordinary media

such as in fluids and gases, the other form of Rankine-Hugoniot relations, expressing the

conservation of mass, momentum, and energy across the discontinuity, were used (Hiermaier

36

2008). The effective variables of state beyond and behind the shock wave front are the pressures

denoted by p0, p1, the densities denoted by ρ0, ρ1, the specific integral energies denoted by e0, e1,

and the particle velocities denoted by u0, u1. The velocity of shock front propagation is denoted

by us. The particle velocity in the medium ahead of the shock wave front is commonly assumed

to be stagnant (u0 = 0). Therefore, the equations of the conservation of mass, momentum, and

energy are stated as:

( ) (3.6)

(3.7)

( )

(3.8)

ANSYS AUTODYN

has both 2D and 3D explicit numerical analysis solvers, known as

"hydrocodes" where the equations of conservations of mass, momentum, and energy (governing

equations) along with material models are simultaneously solved. AUTODYN

integrates finite

difference, finite volume, finite elements, and meshless methods depending on solution needs,

making it particular advantageous to use for modeling explosion, blast wave propagation, and the

interactions between solids and blast waves. The governing equations of explosive detonation,

blast wave generation and propagation in AUTODYN

, are solved by Euler methods (Fairlie

1998, AUTODYN 2003). Various Euler solvers are applied for different needs of numerical

computation. Based on finite volume methods, the multi-material Euler solver uses an

immovable grid and tracks the states and flows of the materials throughout its grid, which

therefore allows for multi-material flows and material strengths to be included in computation.

The multi-material Euler processors in AUTODYN

, also known as Godunov multi-material

high-order Euler solvers, follow the techniques developed by van Leer (1977, 1979). Due to the

high expansion and short time frame of the detonation of high explosives, a two dimensional

37

multi-material Euler solver is used to solve the dynamic gas and fluid problems involving

multiple materials, such as the 2D detonation model constituted by TNT and air in the present

study. The simulation of the 2D detonation model of TNT and air generated blast wave that

transformed from the detonation energy of the TNT explosive, which was ignited in its center.

This is the first step of the entire modeling process of the 3D blast-head simulations of the

present study.

A fast single-material high-order Flux-corrected transport (FCT) 3D Euler processor was

used for the numerical solution of the blast wave propagation through the 3D air space in the

present study. The single-material FCT processor is more efficient at addressing the problems of

shock wave propagations in fluids and gases, and it is based on the algorithm developed by

Zalesak (1979). The states of the 1D blast wave originated from an initial simulation of 2D TNT

detonation can be "remapped" into the 3D Euler-FCT coarser grid filled by fluid or gas material

(with initial internal energy) to continue the numerical simulation of blast wave propagation

through the 3D space (AUTODYN 2003). The "remap" technique for blast simulation provided

by AUTODYN

was developed for two reasons: first, more accurate results of the detonations of

high explosives can be obtained by the 2D multi-material Euler processor using a finer grid

consisting of more cells; second, physical simulation time can be saved because 3D simulation of

shock wave propagation consumes more computational resource than the 2D grid does.

Therefore, a "remap" technique is very suitable for solving the shock wave propagation problems

in a large space or say in the far-field. Once the end states of the 1D initial blast wave model are

imported into the 3D Euler-FCT space, a spherical 3D blast wave model is formed and is

symmetrical to the detonation center specified. Then, the 3D blast wave model is processed as a

38

high-pressure ideal gas region which can continue propagating, reflecting, or coupling with

solids.

The powerful Euler-Lagrange coupling algorithm provided by AUTODYN

solves the

FSI problems encountered in fluid-structure interaction, and in gas-structure interaction, such as

the interaction between a blast wave and a solid structure. The Euler-Lagrange coupling transfers

the loading from the propagating blast wave within the Euler-FCT grid to the impinging solid

structures. Solid structures represented by the Lagrange formulation can "cut" through the fixed

Euler mesh in an arbitrary manner. The Euler cells intersected by the Lagrange interface generate

stress states forming the boundary conditions of the Lagrange interface. In turn, the Lagrange

interface geometrically constrains the mass flow traveling within the Euler grid. The Euler solver

employs a control volume to solve the equations governing the conservations of mass,

momentum, and energy. As the Lagrange grid moves across the interacting Euler grid, the Euler

control volumes can become very small, and even tends to zero when completely covered. To

maintain the stability of the numerical solution, AUTODYN

combines small control volumes

with their large neighbors as new larger control volumes. If a cell becomes sufficiently

uncovered, it can be released as independent (AUTODYN 2003).

AUTODYN

can solve a number of time-varying dynamic problems including blast,

impact, and contact by using the explicit finite element method. The direct time integration

algorithms to solve the equation of motion are commonly classified as explicit or implicit. In

explicit methods, the displacements at future time steps are computed using the information from

previous time steps. The advantage of an explicit-time integration algorithm is that the solution

can be computed without solving a system of equations, therefore this algorithm adapts to a

variety of problem types. In comparison, in implicit-time integration method, the displacements

39

at future time steps depend not only on the past displacements, velocities, and accelerations, but

also on the velocities and accelerations at the time step that is being solved. Therefore, the

implicit algorithm will require the solution of a system of equations at each time step, resulting

in a significant increase in computational demand as compared to explicit algorithm. To date, the

implicit algorithm only applies to limited types of problems.

A drawback of the explicit method is that it is conditionally stable. If the time step is too

big, a stable solution will not be reached. So, a smaller time step is usually indicated for a stable

and accurate solution. AUTODYN

will adjust the time increment during simulation for stability

and accuracy according to the complexity of the simulation at current time step. For the entire

mathematical formulations of the explicit and implicit finite element methods, interested readers

can refer to the books about finite element methods (Belytschko et al. 2000, Hughes 2000).

3.3 MODELING PROCEDURES OF BLAST-HEAD SIMULATION

Three simulation scenarios of human head exposure to blasts were performed. The first scenario

simulated the human head exposures to the blasts from three horizontal orientations, i.e. anterior,

right lateral, and posterior, such that the influence of blast orientations to the injury mechanism

and the associated injury threshold could be analyzed. The second scenario involved the

simulations of the human head exposures to the blast waves coming from the TNT explosions on

the ground. The third scenario of blast-head simulations examined the mechanical responses of

the human head model sustaining blast loadings in a small room. The first simulation scenario

consisted of three blast-head simulation sets which corresponded to the three exposure

orientations respectively. In addition, each simulation set had five blast-head simulations which

40

corresponded to five different intensities of the blast waves from the detonations of 250g, 300g,

350g, 400g, and 450g center-ignited TNT spherical charges at one meter distance from the head.

The ground blast-head simulations and the small room blast-head simulations also used the 250g,

300g, 350g, 400g, and 450g TNT spherical charges.

For each simulation scenario, the full computational model consisted of an idealized air

space consisting of an Euler-FCT grid and the Lagrange FE head model. As shown in Figure 3-1,

the air space was modeled as a 3 m by 1.8 m by 3 m volume meshed by the 30 mm length

hexahedron Euler element. The material property of air was characterized by the ideal gas

material constitutive model and was assigned the internal energy of a standard atmosphere. An

Euler grid maintains its shape while the fluid moves within the grid domain, thus it was suitable

for the numerical simulation of blast wave propagation. The head model was formulated with

Lagrange elements, which deform with the materials contained. Solid material undergoes

relatively smaller deformations than fluid media, so Lagrange elements could better simulate the

mechanical responses of human head.

In order to save the computational expense of the blast wave generation and propagation,

and to obtain a more accurate result, the provided "remapping" tool in AUTODYN

was used to

simulate an initial 2D blast model for every blast scenario. In the 2D TNT air-blast model, the

length of TNT was set to the radius of the 3D TNT spherical charge. The states of the 1D blast

wave obtained from the initial 2D blast were transferred into the 3D air space to construct a

complete 3D spherical blast wave (Figure 3-1b). Before the onset of the blast simulations, the

internal energy of the air space was set to ambient conditions such that the atmospheric pressure

could return to the standard atmosphere after the blast energy fully dissipated from the air space.

41

The complete FE head model was embedded into the 3D air space model for every blast-

head simulation. The neck of the head model was assigned to have a free boundary condition

since this boundary condition was a more realistic reflection of the mobility of the neck during

the blast event. At every time step, the fully coupled Euler-Lagrange algorithm coordinated the

two different numerical formulations of the blast wave and the FE head model, therefore

enabling the blast wave to transmit through the FE head model. In order to monitor the

mechanical responses of the head to blast waves, 23 gauge points, similar to real sensors, were

placed inside the head (Figure 3-2). Particularly, in the SSS region, gauges No. 1, No. 2 and No.

3 were placed in the skull, CSF, and cortex respectively, in order to record the complete

mechanical responses of the three distinct tissue layers surrounding the SSS. Gauges No. 4 to No.

16 were placed in the head at various locations along the anterior-posterior direction in the mid-

sagittal plane, in order to track the evolvement of the intracranial mechanical responses along the

pathway of the blast waves. From gauge No. 6 to gauge No. 13, a distance of 20 mm between

two gauges was specified. Gauge No. 24 was fixed near the head model in the air to track the

pressure-time histories of the blast wave near the head, without any change of location as the

blast specification switched. An additional air gauge was placed in the rear space of the head

model for the room blast-head simulation scenario.

The simulation results were analyzed to identify the patterns of the pressure wave

propagation in the head during the various blast scenarios, and to identify the locations and the

strengths of the high-level volumetric and deviatoric stresses, and to understand how the stresses

evolved during the whole process of blast-head interactions. The intracranial pressures and

deviatoric stresses were used to estimate the injury severities or perhaps thresholds of the

cerebral contusion and DAI, respectively. The mechanical responses of the SSS were used to

42

determine the loading conditions assigned on the independent bridging vein finite element

analysis which would estimate the injury occurrence of the blast-induced subdural hemorrhage.

43

(a)

(b)

Figure 3-1. (a) 2D 450g TNT air-blast model was remapped into the Euler-FCT grid of the air space model in order

to form (b) the complete 3D blast-head model of 450g TNT

44

(a)

(b)

Figure 3-2. Locations of gauges: (a) Sagittal cross-sectional view, (b) Transverse cross-sectional view

45

4.0 BLAST-HEAD INTERACTION SIMULATIONS OF HORIZONTAL EXPOSURE

TO BLAST

This chapter presents the mechanical responses of the human head for the first blast-head

simulation scenario, i.e., the simulations of FE human head subjected to the blast waves from the

anterior, right lateral, and posterior directions. The charges of the TNT explosives were 250g,

300g, 350g, 400g, and 450g for each direction. The sensitivities of the human head responses to

the blast overpressure (BOP) levels and orientations were investigated. The distribution patterns

of the intracranial pressure and the von-Mises stress of the brain model were investigated to

estimate the possible injured cerebral regions. The influences of the impinging BOPs at the blast

incident side and the exposure orientations on the injury severities of cerebral contusion at

various cerebral regions were assessed based on the corresponding levels of the intracranial

pressures. The possibility of diffuse axonal injury (DAI) based on the levels of von-Mises

stresses at the focal regions was also evaluated.

4.1 PREPROCESSING OF SIMULATIONS

The air space model was established as described in the section 3.3. An open boundary condition

was assigned to the surfaces of the 3D air space except the surface where the detonation center

was located such that the blast waves could propagate out of the space without reflection. The

46

boundary condition settings of the air space along with the three pre-processed blast-head models

for the three horizontal blast orientations are shown in Figure 4-1. The six surfaces of the 3D air

space were named according to their locations and orientations in the Cartesian coordinate

system of AUTODYN

, in order to facilitate the following discussions. Among the three

surfaces containing the zero point of the coordinate system, the surface perpendicular to the Y

axis was named as the anterior surface; the surface perpendicular to the X axis was named as the

right lateral surface; the surface perpendicular to the Z axis was named as the bottom surface. In

contrast, among the three surfaces at the distal locations with respect to the zero point, the

surface perpendicular to the Y axis was named as the posterior surface; the surface perpendicular

to the X axis was named as the left lateral surface; the surface perpendicular to the Z axis was

named as the top surface.

The three simulation sets corresponded to the three horizontal blast orientations which

were anterior, right lateral, and posterior, according to the orientations from which the head was

exposed to the blasts. In every simulation set, the FE head was subjected to the spherical air blast

waves generated from the 250g, 300g, 350g, 400g, and 450g spherical TNT blasts. For every

TNT explosive mass, a 2D TNT air-blast model was established to simulate the 1D blast wave

propagating to a one meter distance. The states of the 1D blast waves were then transferred into

the 3D air space to form the 3D spherical blast waves. The FE head model was placed one meter

from the detonation center which was located at the center of the anterior surface of the air space.

The durations of all the fifteen blast-head simulations were set to 5 ms, which was adequate for

the typical Friedlander wave to fully exhibit and to dissipate completely from the air space. The

simulations represented the ideal scenario where a people horizontally experienced the open-

47

field blasts with various explosive intensities from the three principal directions at the same

horizontal level.

48

(a)

(b)

Figure 4-1. (a) The five surfaces of the air space were assigned with the open boundary condition indicated by

orange color, (b) The FE head model was exposed to the blasts from the anterior, posterior, and right lateral

horizontal orientations

49

4.2 BRAIN PRESSURE RESPONSE TO HORIZONTAL BLAST

The time-lapse illustration of the 250g TNT anterior blast-head simulation in the mid-sagittal

plane shows that the shock front of the 3D spherical blast wave expanded and propagated purely

along the radial direction (Figure 4-2). The pressure time histories of blast overpressure (BOP)

and the typical intracranial pressure time histories at several intracranial sites are shown in

Figure 4-3. Behind the shock front, the dipping of the ambient pressure below standard

atmospheric pressure, i.e. under-pressure, was observed. When the shock front propagated across

the head, a slight wave reflection formed at the front of the head (Figure 4-2b). This reflection

caused the small curvilinear inflection in the pressure time histories given in Figure 4-3a (the

pressure produced by the gauge in front of the head in air) between approximately 0.3-0.5s.

Judging from the very modest reflection and the discontinuity of high-level pressure behind the

head (Figure 4-2d), it is believed that most of the energy of the blast wave impinging on the head

was absorbed, resulting in the pressure waves propagating inside the head. The small reflected

portion where the shock front reached the head and the discontinuity of high-level pressure

behind the head were also observed in the blast-head simulations of the other two blast

orientations.

50

(a) (b)

(c) (d)

Figure 4-2. Blast wave propagating through the head during the first 0.5 ms of the 250g TNT blast-head simulation

of the anterior blast scenario: (a) 0.2 ms, (b) 0.4 ms, (c) 0.5 ms, (d) 0.75 ms

reflection

51

The pressure waveforms of the blast waves in open-space air of the fifteen simulations

were typical Friedlander waves (Friedlander 1976), which began with a sharply rising over-

pressure followed by an under-pressure, finally returning to the normal ambient pressure after the

subsidence of the blast energy (Figure 4-3a). The magnitudes of the BOPs recorded outside the

head at the blast incident side were several times that of the standard atmospheric pressure. As

the TNT weight increased, the peak BOP at the incident side grew as well (Figure 4-3a). The

250g, 300g, 350g, 400g, and 450g TNT charges had BOPs of 291 kPa, 321 kPa, 349 kPa, 379

kPa, and 413 kPa, respectively (Figure 4-3a). In every horizontal blast-head simulation, gauge

No. 24 was kept at the same location in the air space, so the recorded peak BOP value

corresponding to each blast level remained the same for every blast orientation. The total

duration of the apparent BOP pulse lasted about 0.8 ms for every blast.

The pressure time histories of the various intracranial locations exhibited a pattern that

was similar to that of the ambient pressure-time history: the intracranial pressures began with

sharply rising and falling to form a pulse, which thereafter returned to zero pressure. Higher peak

BOPs caused higher peak positive pressures in the brain for most intracranial locations, while the

duration of the pressure pulse at the same cerebral location remained the same. The pressure

pulse durations at the various intracranial sites were primarily related to the locations. The

pressure pulse duration on the side of the head that was proximal to blast was smaller than that

on the distal side to blast. The magnitude of the pressure wave attenuated during its propagation

from the proximal to distal side of the head. For example, for the 300g TNT case for the anterior

blast exposure, the peak positive pressure recorded by the gauge No. 6 at the frontal cortex was

201 kPa, while the gauge No. 14 at the occipital cortex had 138 kPa, so the corresponding

percentage of attenuation in magnitude was calculated to be 31 %.

52

(a) (b)

(c) (d)

(e) (f)

Figure 4-3. Pressure-time histories recorded by various gauge points for the anterior blast-head simulations: (a) No.

24 in atmosphere (b) No. 2 in the CSF at SSS, (c) No. 6 on the frontal cortex, (d) No. 14 in the occipital cortex, (e)

No. 18 at the posterior margin of the tentorium cerebelli, (f) No. 19 on the lower brainstem

53

The highest value and the lowest value of the peak positive pressures existed on the

proximal blast area and on the distal blast area of the brain, respectively, for all the simulations.

Within the anterior blast exposure cases, the highest values of peak intracranial pressure occurred

at the frontal cortex (gauge No. 6), ranging from 161 kPa to 308 kPa, while the lowest values

occurred at the midsagittally posterior parietal area (gauge No. 12), ranging from 87 kPa to 94

kPa. Among the gauges from No. 6 to No. 14, the peak positive pressures for the gauges No. 6 to

No. 12 exhibited an apparent gradient of the peak pressure attenuation, while gauges No. 12 to

No. 14 exhibited a slight increasing gradient of peak pressure, as the areas of their corresponding

coronal cross sections of the brain decreased. The peak pressures recorded by the gauge No. 14

for the anterior blast exposure ranged from 132 kPa to 142 kPa. The mitigation of the intracranial

pressure indicated that the pressure wave traveling in the head has some blast energy absorbed

by the viscoelastic brain tissue. The pressure wave attenuation was also obvious in the simulation

sets of the right lateral blast exposures and the posterior blast exposures. Because the skull

chamber was broader in the middle and was narrower in the front and back, the levels of the

intracranial pressure waves were reinforced as they traveled from the broader cerebral cross-

section to the narrower one, as long as the attenuation effects of the brain tissue was

comparatively secondary to the concentration effect of the narrow region in the present

simulations.

There was a timing delay between the arrival times of the peak positive pressures at the

proximal blast location and at the distal blast location in the brain. For the anterior blast

simulation set, the timing delay was 0.44 ms for gauge No. 6 and No. 14 (Figure 4-3c and Figure

4-3d); for the right lateral blast simulation set, the timing delay was 0.25 ms between gauges No.

22 and No. 23; for the posterior blast simulation set, the timing delay was also 0.44 ms between

54

gauge No. 14 and No. 6. The timing delay was interpreted as the time for the intracranial

pressure wave to propagate from the proximal blast side to the distal side in the brain. The peak

positive pressure in the CSF at SSS of gauge No. 2 did not show a notable difference among the

three blast orientations while the anterior blast simulation set had a slightly higher level.

Therefore, the peak pressures of gauge No.2 of the anterior blast simulation set were taken as the

input loadings on the bridging vein finite element model to later estimate the injury occurrence

of subdural hemorrhage instead of simulating bridging vein responses for all the three blast

orientations.

In the cortex, the right lateral exposure orientation to the blasts had the highest levels of

cortex pressures at the proximal side, i.e. right temporal cortex, with the range from 240 kPa to

421 kPa (gauge No. 22), as compared to 221 kPa to 402 kPa at the occipital cortex (gauge No. 14)

of the posterior blast exposure simulation set, and to 161 kPa to 308 kPa at the frontal cortex

(gauge No. 6) of the anterior blast exposure simulation set. The most injurious loading direction

for cortex predicted for the horizontal blasts is very similar to the published bTBI simulation

study of Taylor and Ford (2009), who revealed that the lateral blast was more injurious than the

frontal and posterior blasts.

In the brainstem, the posterior exposure orientation to the blasts had the highest pressure

levels, with the range from 247 kPa to 446 kPa, among the three orientations. In the posterior

exposure cases, the pressure levels on the lower brainstem were even higher than that on the

occipital cortex. The pressure waves propagating into the lower brainstem were reinforced by the

concentration effect of the foramen magnum, which had a narrow region, even though the lower

brainstem and the occipital cortex were both proximal to the blast waves. The lower brainstem in

55

the posterior blast exposures had the highest intracranial pressures among all the cerebral

locations for the three blast exposure orientations.

Figure 4-4 shows the distribution of the intracranial pressure wave in the brain from 0.2

ms to 0.8 ms for all the blast orientations. For each of the blast orientations, the high pressure

region of the brain first occurred at the proximal side to the blast wave source, then moved to the

central cerebral region, and finally occurred at the side which was distal to the blast source. The

pressure wave propagation within the cranium was associated with a decreasing gradient in

pressure magnitude for each blast orientation. The highest pressure always occurred in the

cerebral regions which were proximal to the blast wave source for each orientation, so the

severity of parenchymal injury is expected to be a function of proximity to the blast wave source.

A high-level positive and negative pressure existed at the lower brainstem and spinal cord for all

the three blast orientations. The intense compressive and tensile pressures as well as their sharp

transition in the posterior fossa and foramen magnum, especially for the inferior aspect of the

cerebellum, pons, medulla and cervical spinal cord, could make the parenchyma and vasculature

particularly vulnerable to injury.

56

Figure 4-4. Pressure distributions of the brain in the 400g TNT blast-head simulations of all blast orientations

Anterior blast orientation

0.2 ms 0.40 ms 0.56 ms 0.80 ms

Right lateral blast orientation

0.2 ms 0.40 ms 0.50 ms 0.80 ms

Posterior blast orientation

0.2 ms 0.40 ms 0.50 ms 0.80 ms

57

The pressure distribution patterns of the blast-induced TBI were distinct from that of the

blunt impact induced TBI that exhibited a typical “coup and contrecoup” pressure phenomenon,

in which the high level positive pressure prevailed at the impact side while high level negative

pressure with similar magnitude prevailed at the opposite impact site of the brain simultaneously.

The high negative pressure at the contrecoup side developed as the skull pulls the brain along

due to the relative skull-brain motion resulted from the blunt impact on the cranium. In the

simulation study of impact TBI published by Zhang et al. (2004), the predicted peak pressures at

the coup and contrecoup sites ranged from 43 kPa to 130 kPa in compression at coup side, and

from 32 kPa to 128 kPa in tension at contrecoup side. The pressure range at the coup cerebral

region and that at the countercoup cerebral region were revealed to have nearly equal values. In

contrast, in the present study, the anterior blast scenario possessed significantly higher peak

positive pressures that ranged from 160 kPa to 308 kPa on the proximal side of the head, and the

corresponding peak negative pressures were comparably lower in magnitude, ranging from -99

kPa to -127 kPa (Figure 4-3c); at the distal side from the blast (occipital cortex), the peak

positive pressures still existed with a range from 132 kPa to 142 kPa which were still higher in

magnitudes than the corresponding peak negative pressures ranging from -66 kPa to -76 kPa.

The principal that the positive pressure was several times the magnitude of the negative pressure

in the cranium applied to every blast orientation. Hence, it is concluded that the “coup-

countrcoup” intracranial pressure mechanism does not apply to the bTBI. Instead, the

propagation of the intracranial pressure waves induced by the direct blast wave transmission into

the head is the pressure distribution pattern of the bTBI.

In a published study by Ward et al. (1980), an intracranial pressure injury index was

proposed to evaluate the occurrence and the injury severity of cerebral contusion. According to

58

this intracranial pressure tolerance criterion/index, the peak intracranial pressure of more than

235 kPa would induce serious cerebral contusion, while minor or no brain injuries would occur

when the intracranial pressure was below 173 kPa. In between 173 kPa and 235 kPa, minor

contusion or cortex hemorrhage would occur. Predicted intracranial pressure responses at the

proximal side (frontal cortex) for all the blast simulation cases of the anterior blast exposure,

except the 250g TNT case, were higher than 173 kPa, and the 400g TNT case had 252 kPa peak

pressure which was more than the 235 kPa serious injury threshold. Therefore, people

experiencing the anterior blast waves with the impinging BOP at the blast incident side from 321

kPa to 349 kPa would have a risk of suffering a minor contusion or cerebral cortex hemorrhage,

and people experiencing the anterior blast wave with the impinging BOP at the blast incident

side more than 379 kPa would be expected to have serious cerebral contusion. All the blast-head

simulations of the right lateral blast exposures had peak positive pressures of more than 235 kPa

at the cortex region proximal to the blast (right temporal cortex), indicating that people

experiencing the lateral blast wave with the impinging BOP of more than 291 kPa at the blast

incident side would have serious cerebral contusion. In the posterior blast cases, the peak

positive pressures at the proximal side (lower brainstem) were all more than 235 kPa. Therefore,

people experiencing the posterior blast wave with the impinging BOP of more than 291 kPa

would have serious cerebral contusion.

The injury severities of the various cerebral locations including the cortex at the SSS,

frontal cortex, occipital cortex, temporal cortexes, hypothalamus, and lower brainstem with

respect to the five impinging BOPs at the blast incident side for the three blast exposure

orientations are summarized in Table 4-1 (anterior exposure), Table 4-2 (right lateral exposure),

and Table 4-3 (posterior exposure). For a better illustration, predicted contusion injury locations

59

and the associated severities for the three exposure orientations were pointed out on the mid-

sagittal view of the brain in the Figure 4-5 (anterior exposure), Figure 4-6 (right lateral

exposure), and Figure 4-7 (posterior exposure).

60

Table 4-1. Predicted contusion injury severities at typical cerebral sites with respect to impinging BOPs at the blast

incident side in the anterior blast-head simulations

Peak BOP

(TNT weight)

Cortex

at SSS

Frontal

cortex

Occipital

cortex

Temporal

cortexes

Hypothalamus Lower

Brainstem

291 kPa (250g) None None None None None None

321 kPa (300g) Minor Minor None None None None

349 kPa (350g) Minor Minor None None Minor Minor

379 kPa (400g) Serious Serious None Minor Minor Minor

413 kPa (450g) Serious Serious None Minor Serious Minor

Figure 4-5. Predicted contusion injury location and severity of the anterior blast-head simulations

ICP 235 kPa - Serious Contusion

ICP 173 kPa - Minor Contusion

BOP 291 kPa

BOP 321 kPa

BOP 349 kPa

BOP 379 kPa

BOP 413 kPa

Temporal cortexes:Minor contusions for BOP 379 kPa and 413 kPa

61

Table 4-2. Predicted contusion injury severities at typical cerebral sites with respect to impinging BOPs at the blast

incident side in the right lateral blast-head simulations

Peak BOP

(TNT weight)

Cortex

at SSS

Frontal

cortex

Occipital

cortex

Temporal

cortexes

Hypothalamus Lower

Brainstem

291 kPa (250g) None Minor None Serious None Minor

321 kPa (300g) None Minor Minor Serious None Serious

349 kPa (350g) Minor Serious Minor Serious Minor Serious

379 kPa (400g) Minor Serious Minor Serious Minor Serious

413 kPa (450g) Minor Serious Serious Serious Minor Serious

Figure 4-6. Predicted contusion injury location and severity of the right lateral blast-head simulations

Temporal cortexes:Serious contusions for all predicted BOPs

ICP 235 kPa - Serious Contusion

ICP 173 kPa - Minor Contusion

BOP 291 kPa

BOP 321 kPa

BOP 349 kPa

BOP 379 kPa

BOP 413 kPa

62

Table 4-3. Predicted contusion injury severities at typical cerebral sites with respect to impinging BOPs at the blast

incident side in the posterior blast-head simulations

Peak BOP

(TNT weight)

Cortex

at SSS

Frontal

cortex

Occipital

cortex

Temporal

cortexes

Hypothalamus Lower

Brainstem

291 kPa (250g) None None Minor None None Serious

321 kPa (300g) None None Serious Minor None Serious

349 kPa (350g) Minor None Serious Minor None Serious

379 kPa (400g) Minor None Serious Serious Minor Serious

413 kPa (450g) Minor None Serious Serious Minor Serious

Figure 4-7. Predicted contusion injury location and severity of the posterior blast-head simulations

Temporal cortexes:• Minor contusions for BOP

321 kPa and 349 kPa• Serious contusions for BOP

379 kPa and 413 kPa

BOP 291 kPa

BOP 321 kPa

BOP 349 kPa

BOP 379 kPa

BOP 413 kPa

ICP 235 kPa - Serious Contusion

ICP 173 kPa - Minor Contusion

63

The lateral blast exposure was the most injurious orientation to the cortex among the

three exposure orientations for the same blast severity, while the posterior exposure was the most

injurious orientation to the lower brainstem. The lower brainstem is shown to be particularly

vulnerable to have contusion in bTBI because the pressure waves were ultimately funneled into

the foramen magnum and the vertebral column for every blast scenario (Figure 4-4), which

subjected the inferior cerebellum, medulla and spinal cord to large pressure fluctuations.

Although the positive peak pressure responses along the brainstem were similar to that of the

cortex that was proximal to the blasts in the right lateral and posterior orientations, they created

additional risks for injuries because the superficial veins along the anterior surface of the

brainstem were likely to be vulnerable to injury. The posterior fossa area with the large peak-

peak pressure differences contained the intracranial portion of the vestibulo-cochlear and

trigeminal nerves, which, if damaged, could contribute to the dizziness, hearing loss and

headache that were observed acutely with mild blast TBI (Hoffer et al. 2013, Hoffer et al. 2013).

The intracranial pressure injury index of Ward et al. (1980) was stated as applicable to cerebral

contusion, so, for the injuries of the spinal cord, this criterion may not apply. Therefore, this

pressure-based injury criterion was not used in the present study for injury severity analysis of

the spinal cord. A detailed quantitative assessment of spinal cord injury severity would be

discussed once its widely recognized injury criterion became available.

In the literature of impact TBI, relative motion between the skull and brain has been

validated as a cause of subdural hemorrhage during the impact or acceleration events (Gennarelli

and Thibault 1982, Depreitere et al. 2006). Magnitudes of the relative skull-brain motion during

impact and quasistatic circumstances have been assessed quantitatively by using in vivo MRI

techniques (Feng et al. 2010, Monea et al. 2012). However, in the present study using the finite

64

element simulations, it was found no predicted relative displacement existed between the skull

and the cortex at the SSS during the transient blast wave propagation through the head (zero

displacement plots are not shown here). Therefore, unlike for the TBIs induced by impact or

acceleration, primary bTBI is conjectured to not be caused by the relative motion between the

skull and brain. The combination of this fact and the foregoing discussions of the pressure

distribution pattern of bTBI consolidates our conclusions that the bTBI injury mechanism is

primarily attributed to the propagation of the intracranial pressure wave induced by the direct

transmission of the blast wave into the cranium and that the "coup-contrecoup" injury

mechanism observed for impact- or acceleration-induced TBIs (Hardman and Manoukian 2002,

Zhang et al. 2004) does not apply to bTBI.

4.3 BRAIN SHEAR STRESS RESPONSE TO HORIZONTAL BLAST

Von-Mises stress was taken as the indicator of the cerebral shear stress analysis for the present

study. By examining the shearing responses throughout the brain in all the fifteen simulation

cases, the cortex, brainstem, and spinal cord were found to be the primary locations that

experienced high-level shear stresses, and the inner brain had the lowest shear stresses, which

were all less than 0.1 kPa. It is believed that the density difference between the brain matter and

the CSF caused the sliding over one another, stretching the neurons that traverse the interfaces

between the areas of different densities. This sliding force between the brain and the CSF caused

high-level shear stress at the cerebral surface adjacent to the CSF, whereby the intracranial

tissues absorbed the kinematic energy of the blast wave transferred to them. The cortico-

medullary junction (gray matter-white matter junction) experiencing high-level shear stresses

65

contained significant amounts of the neuron axons, which connected the gray matter and white

matter, and thus appear to be particularly vulnerable to shear stresses. These in turn, caused DAI

lesions by stretching, separating, and disrupting the nerve fiber tracts (Taber et al. 2006,

McAllister 2011).

Like the pressure responses, for the same cerebral location, the pattern of the time-history

of von-Mises stress remained the same as the blast strength varied, although the peak von-Mises

stress increased with increasing blast strength. For every simulation case, the peak shear stresses

in the brainstem and spinal cord were higher than that in the cortex. In the anterior blast cases,

the highest von-Mises stresses of cortex occurred at the frontal region (gauge No. 6) with the

peak values ranging from 0.73 kPa to 1.10 kPa; for the right-lateral blast cases, the highest von-

Mises stresses in the cortex occurred at the right temporal region (gauge No. 22) with the peak

values ranging from 1.09 kPa to 1.58 kPa; in the posterior blast cases, the highest von-Mises

stresses of cortex occurred in the right temporal region (gauges No. 22) with the peak values

ranging from 0.74 kPa to 1.18 kPa. The anterior blast cases had the highest shear stresses at the

lower brainstem/medulla oblongata with peak values ranging from 1.55 kPa to 2.81 kPa, whereas

the right lateral and posterior blast cases had the highest shear stresses in the spinal cord, which

have peak values ranging from 1.33 kPa to 2.06 kPa, and from 1.48 kPa to 2.10 kPa, respectively.

The spinal cord was not the point of interest of this study, so the injury analysis of DAI did not

include the results of the spinal cord.

The von-Mises stress results of all the fifteen horizontal blast-head simulations are not

shown here. As a typical example, the time histories of von-Mises stress for the gauges No. 6,

No. 14, No. 22, and No. 23 at the cortex in the 450g TNT cases are shown in Figure 4-8. In each

of the blast orientations, the von-Mises stress time histories at some of the cortex locations

66

showed a "impulse-like" pattern, i.e. a similar pattern of the BOP and the intracranial pressure

time histories, such as the gauges No. 6 and No. 23 in the anterior blast cases, the gauge No. 6 in

the right lateral blast cases, and the gauge No. 23 in the posterior blast cases. Despite of the

“impulse-like” time history pattern of the von-Mises stresses of some cerebral locations, the time

histories of von-Mises stresses of several cerebral locations still developed after 1 ms throughout

the whole simulation time, showing a time history pattern quite different from the “impulse-like”

pattern of the intracranial pressure-time histories. Figure 4-9 shows the time histories of von-

Mises stresses on the lower brainstem of the three 450g TNT blast-head simulations of three

exposure directions, along with the corresponding intracranial von-Mises stress distributions at

the occurring times of the peak von-Mises stresses at the lower brainstem of the three

orientations. Because the foramen magnum contained the anatomic structures with different

densities in this limited space, which could concentrate more energy from the blast, the lower

brainstem did not show any clear or unique pattern of the von-Mises stress time histories which

developed and maintained high levels through the whole simulation time (Figure 4-9a). The

concentration of high von-Mises stresses on the cerebral tissues adjacent to the CSF is clearly

revealed in every blast orientation (Figure 4-9b).

67

(a) (b)

(c)

Figure 4-8. von-Mises stress time histories of the gauge points No. 6 (frontal cortex), No. 14 (occipital cortex), No.

22 (right temporal cortex), and No. 23 (left temporal cortex) in the 450g TNT blast-head simulation cases: (a)

Anterior blast orientation, (b) Right lateral blast orientation, (c) Posterior blast orientation

68

Figure 4-9. von-Mises stress time-histories of gauge No. 19 at lower brainstem and the associated von-Mises stress

distributions showing peak von-Mises stresses in the 450g TNT blast-head simulation cases: left - anterior

orientation (2.45 ms), middle - right lateral orientation (1.85 ms), right - posterior orientation (3.43 ms)

69

Among all the three simulation sets, the anterior blast-head simulations had the highest

values of peak von-Mises stresses at the lower brainstem/medulla oblongata. The right lateral

blast-head simulations had two primary intracranial sites (right temporal cortex and lower

brainstem/inferior cerebellum within the posterior fossa) experiencing high-level von-Mises

stresses with similar magnitudes. Similar to the anterior blast scenario, the posterior blast

scenario had high-level von-Mises stress at the lower brainstem site, but the magnitudes were

lower. Shear stress was proposed as the primary injury predictor of axonal injury for impact TBI

in the study of Zhang et al. (2004), who estimated the tolerable von-Mises stress levels within the

brainstem to be 6.0 kPa, 7.8 kPa, 10.0 kPa for 25%, 50%, 80% probability of mild TBI. The

highest value (2.81 kPa) of von-Mises stress in the present study was much lower than this

axonal injury criterion, therefore, it is hypothesized that shear stress might not be the primary

injury causation of blast TBI as opposed to intracranial pressure. However, without the direct

evidence from clinical study or a rigorous quantitative study relating axonal damage to specific

pressure and shear stress levels, it was hard to conclude which type of mechanical responses in

the brain was the primary TBI causation.

70

5.0 BLAST-HEAD INTERACTION SIMULATIONS OF EXPOSURE TO GROUND

BLAST

This chapter presents the second blast-head simulation scenario, which simulated a person (only

the human head was modeled) experienced the blast waves generated from a variety of TNT

detonations the near ground in front of the person. The charges of the TNT detonations were still

250g, 300g, 350g, 400g, and 450g. The patterns of the blast waves and the intracranial pressure

waves were analyzed. The regions with highest injury in the human head were found to be the

lower brainstem and the frontal cortex, which were closest to the impinging blast waves. The

injury severities of cortical contusions in the ground blast scenario were estimated based on the

predicted intracranial pressure levels. The high shear stresses (von-Mises stresses) distributed on

the surface of the whole brain model. The frontal and temporal cortexes sustained the highest

amounts of shear stresses. Based on the available axonal injury criterion based on von-Mises

stress, shear stress was conjectured as the inferior injury causation as opposed to intracranial

pressure.

5.1 PREPROCESSING OF SIMULATIONS

The air space Euler-FCT model was established as described earlier in the section 3.3, therefore

the dimension, mesh, and material properties of the air space model were the same as that used in

71

the simulations of horizontal blasts. The bottommost surface of the 3D air space model was left

as a closed boundary condition, and all other five surfaces were assigned as open boundary

conditions which let the blast waves propagate out of the space in order to make the simulated

blasts comparable to the real free-field blasts. The closed boundary condition of Euler-FCT mesh

reflects any blast wave toward it back to the mesh, thus the bottommost surface of air space

performed like an actual reflective ground plane in the battle field.

The detonations of the five TNT charges were modeled as five 2D spherical air blasts of

200 millimeter radius in AUTODYN

. Then the state information of each air blast 2D model

was transferred into the 3D air space to form an initial 3D spherical air blast model for each of

the five ground blast-head simulations (Figure 5-1a). In the 3D air space, the detonation center of

each spherical blast was located 200 millimeter vertically away from the ground surface, also

had the x-z coordinate coincident with that of the center of the ground surface. In sum, the

coordinate of the detonation center was (1500 mm, 200 mm, 1500 mm).

The person exposed to ground blasts was modeled to be 1.62 meters high and the face

was a 150 mm distance from the detonation center along the z direction (Figure 5-1b). A gauge

point was placed in the 3D space above the blasts. In addition, the location of the air gauge was

kept the same as that in the simulations of horizontal blast exposures in order to quantify the

extent that the pressure levels of the blasts which were reinforced by ground reflections. The

twenty-three gauges in the FE head model were kept at the same locations as these in the

simulations of horizontal blast exposures. The bottom of the neck was not assigned any

restriction. The duration of every ground blast-head simulations was set to 5 milliseconds.

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(a)

(b)

Figure 5-1. Ground blast exposure simulation scenario: (a) 3D view, (b) Y-Z plane view

Head

Blast

Head

Blast

73

5.2 BRAIN PRESSURE RESPONSE TO GROUND BLAST

Similar to the explosions in the open space, the ground explosion formed a hemispherical blast

wave expanding and propagating radially in the 3D air space, taking the 250g TNT ground blast-

head simulation as an illustrative example (Figure 5-2). At the beginning of the simulation, the

bottom half of the initial spherical blast wave traveled toward the ground. Upon the initial blast

wave reaching the ground, it was then reflected back to the space above. The reflected blast wave

reinforced the initial blast wave and formed a new hemispherical blast wave which had a higher

pressure level near the ground (the lower part of the entire blast wave). In the lower part, the

initial blast wave completely merged with the reflected wave to form a single shock front which

propagated horizontally. While in the upper part of the blast wave, the reflected wave did not

fully merged with the initial blast wave due to the distance between the shock fronts of the initial

and reflected blast waves. This made a secondary blast wave behind the initial blast wave (Figure

5-2).

The blast wave impinged the head model from below. Relative skull-brain motion was

not observed during the process of the blast wave-head interaction. The time lapse pressure

distribution of the brain in Figure 5-3 shows that the high pressure region transmitted from the

spinal cord to the brainstem, and then to the cerebellum and cerebrum. In the ground blast

scenario, the blast incident regions were the spinal cord, brainstem, cerebellum, and frontal lobe,

which had higher levels of positive pressure than those of the distal regions including the parietal

and occipital lobes. In the transmission of the intracranial pressure wave, the magnitude

attenuation of the positive pressure was remarkable. The spinal cord exhibited high pressure

levels in terms of both positive and negative pressure.

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Figure 5-2. Blast wave propagating during the first 1.2 ms of the 250g TNT ground blast-head simulation

0.1 ms 0.45 ms

1.0 ms 1.2 ms

Lower Part

Higher Part

Secondary Blast Wave

Initial Blast Wave

75

Figure 5-3. Pressure distributions of the brain in the 250g TNT ground blast-head simulation from 1.3 ms to 1.8 ms

1.3 ms 1.4 ms 1.5 ms

1.6 ms 1.7 ms 1.8 ms

76

Except for the parietal lobe, various intracranial locations had the wave patterns that were

similar to that of the ambient blast wave. In these locations, the typical pattern of the pressure-

time histories contained a main crest which possessed the peak positive pressure. The pressure

time histories of the BOPs at some proximal locations had two crests (Figure 5-4c to Figure

5-4f). The first crest corresponded to the peak positive pressure of the initial blast wave, while

the second crest corresponded to the secondary blast wave. The initial blast wave had a much

higher pressure level than that of the secondary blast wave. With the increase of the TNT mass,

the peak positive pressures of both the first and second wave crests increased and occurred

earlier. The peak BOP value recorded for the smallest, 250g TNT charge, was about 4 times (419

kPa) of the standard atmospheric pressure, while that of the second crest was 169 kPa (Figure

5-4a). The ambient pressure eventually returned to the standard atmospheric pressure after the

blast energy in the air space completely dissipated.

Higher peak BOPs caused higher peak positive pressures that occurred earlier in time in

the proximal cerebral locations, while the pulse durations remained basically the same. However,

in the CSF at the SSS, a distal cerebral location in the ground blast-head simulations, increased

TNT mass did not increase the value of the peak positive pressure, instead, it increased the area

that the main crest enveloped and increased the amplitude of the peak negative pressure (Figure

5-4b). In every ground blast-head simulation, the amplitude of the peak negative pressure was

bigger than that of the peak positive pressure in the CSF at SSS. In contrast, at most intracranial

locations proximal to blasts, the peak negative pressures had higher amplitudes than for the SSS,

but they were lower than their respective positive pressures (Figure 5-4c to Figure 5-4f).

77

(a) (b)

(c) (d)

(e) (f)

Figure 5-4. Pressure-time histories recorded by various gauge points of the five ground blast-head simulations: (a)

No. 24 in atmosphere (b) No. 2 in the CSF at SSS, (c) No. 6 on the frontal cortex, (d) No. 14 on the occipital cortex,

(e) No. 19 on the lower brainstem, (f) No. 21 on the hypothalamus

78

The pressure ranges of the typical cerebral sites are summarized in the Table 5-1, from

which, it can be seen that the peak positive pressures at the locations of the side proximal to blast

were higher than that of the distal side. The difference in the peak positive pressures between the

proximal side and the distal side of the ground blast-head simulations was similar to that of the

horizontal blast-head simulation scenario due to the same attenuation effect of the viscoelastic

brain parenchyma.

Table 5-1. Pressure ranges in kPa at various cerebral locations: No. 3 (cortex at SSS), No. 6 (frontal cortex), No. 11

(brain parenchyma), No. 14 (occipital cortex), No. 19 (lower brainstem), No. 21 (hypothalamus), No. 22 (right

temporal cortex)

TNT

mass

Gauge Number

No.3 No.6 No. 11 No. 14 No. 19 No. 21 No.22

250g [-55 to 57] [-66 to 117] [-30 to 58] [-53 to 60] [-69 to 143] [-38 to 84] [-35 to 91]

300g [-62 to 58] [-82 to 136] [-30 to 69] [-56 to 69] [-71 to 165] [-41 to 96] [-40 to 103]

350g [-69 to 58] [-97 to 151] [-32 to 77] [-61 to 79] [-77 to 187] [-43 to 107] [-45 to 113]

400g [-74 to 57] [-112 to 174] [-37 to 91] [-71 to 93] [-87 to 215] [-47 to 123] [-57 to 129]

450g [-78 to 55] [-119 to 187] [-41 to 98] [-76 to 101] [-86 to 231] [-48 to 134] [-63 to 137]

At the cerebral locations of the proximal side, the peak positive pressures were several

times the amplitudes of the peak negative pressures. In comparison, at the distal side, the

amplitudes of the peak positive pressures were very close to that of the peak negative pressures.

Taking the 450g TNT ground blast-head simulation as an example, in the lower brainstem

(gauge No. 19), the peak positive pressure was 231 kPa, which was almost three times of the

amplitude of the peak negative pressure -86 kPa; whereas, in the occipital cortex (gauge No. 14),

the peak positive pressure was 101 kPa, which was just 25 kPa more than the amplitude of the

peak negative pressure was -76 kPa. At the cortex of SSS (gauge No. 3), except for the 250g

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TNT case, the amplitudes of peak negative pressures were bigger than the peak positive

pressures. Because the peak negative pressures developed after the blast wave propagated

through the brain, the residual strain energy in the brain was speculated to be the cause of the

negative pressures, indicating that tensile stress was the dominant cause of injury in the parietal

cortex when blasts took place on the ground.

The lower brainstem experienced the highest peak positive pressures with the magnitudes

ranging from 143 kPa to 231 kPa. This range was very close to that observed for the lower

brainstem in the horizontal blast-head simulation scenario, despite of the longer head to blast

source distance in the ground blast-head simulation scenario. The frontal cortex experienced the

second highest level of peak positive pressures with the range being from 117 kPa to 186 kPa.

This range was far below that of the horizontal and right lateral blast-head simulations. This

large pressure difference in the same location between the ground blast scenario and the two

horizontal blast-head simulation sets can be attributed to the longer distance from the blast center

to the head and the protection of the head structure beneath the forehead in the ground blast

scenario. However, the peak positive pressures of the frontal cortex in the 400g TNT and 450g

TNT cases of the ground blast scenario were higher than that of the posterior blast scenario.

Among all the intracranial locations, the frontal cortex tolerated the highest level of peak

negative pressures ranging from -66 kPa to -119 kPa, which was considered less harmful to the

brain than the associated positive intracranial pressures, which had higher magnitudes.

The internal brain parenchyma had its maximum positive pressures below 100 kPa and its

maximum negative pressures above -50 kPa. The relatively low pressure conditions of the

internal brain in the ground blast scenario were similar to that of the horizontal blast scenario,

addressing the internal brain as the "safe region". An interesting outcome here is that

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hypothalamus, though proximal to the blast, did not experience significant peak positive

pressure. This could be attributed to the protection of the two skull layers on the pathway that the

blast waves propagated to the hypothalamus. The temporal lobes experienced similar amounts of

both positive and negative pressures to that of the hypothalamus.

The contusion injury severity and occurrence at various cerebral regions in the ground

blast-head simulations were assessed using the cortical contusion criterion suggested by Ward et

al. (1980). None of the cerebral locations had peak positive pressure of more than 235 kPa, the

pressure level that induced the severe contusion. However, the frontal cortex in the 400g and

450g cases, and the lower brainstem in the 350g, 400g, and 450g cases were subjected to positive

pressures above 173 kPa, therefore minor contusions would occur in the lower brainstem once

the TNT mass exceeded 350g and in the frontal cortex once the TNT mass was more than 400g.

The "coup-contrecoup" injury pattern was still not observed in the ground blast-head

scenario. However, at the distal side of the brain including the parietal and occipital cortexes, the

peak positive pressures (compression) and the peak negative pressures (tension) occurred

sequentially with equivalent magnitudes. This kind of compression to tension transition in the

ground blast scenario was more obvious than for the horizontal blasts scenario, and thus could

decrease the injury tolerance of the brain tissue at the distal side. In comparison, the impact

induced TBI has the compression and tension with equivalent levels occurring simultaneously at

the coup side and the contrecoup side, respectively (Zhang et al. 2004). Again, the posterior

fossa was found to be the "vulnerable region", which subjected the inferior aspect of the

cerebellum, pons, medulla, and cervical spinal cord to high positive pressures. It was expected

that if the TNT charges of the ground blasts exceed a certain amount, the high level pressures at

81

the posterior fossa could injure its associated parenchyma and vasculature, for example causing

brainstem hemorrhage.

5.3 BRAIN SHEAR STRESS RESPONSE TO GROUND BLAST

The shear stress analysis here is based on the von-Mises stress of brain. The brain experienced

the highest amounts of shear stresses during the time range from 1.6 ms to 2.1 ms. As a typical

example to illustrate the distributions of the von-Mises stresses, the time-lapse distributions of

cerebral von-Mises stresses shown in the sagittal cross-sectional view for the 250g TNT ground

blast-head simulation are depicted in Figure 5-5 at different times ranging from 1.6 ms to 2.1 ms

in 0.1 ms intervals. The brain cortex, lower brainstem, lower cerebellum, spinal cord, and any

other regions adjacent to the CSF, were again revealed to be the primary locations experiencing

high level von-Mises stresses, i.e. the concentration of high shear stresses. In comparison, the

central parenchyma experienced relatively low level shear stresses (Figure 5-5). In the core

region of the central parenchyma, the von-Mises stresses were below 0.1 kPa for all the five

simulations.

Although the spinal cord had much higher von-Mises stress than the other parts, it is not

included in the discussion for TBI of the current study because the spinal injury is not considered

as a topic of bTBI. However, it is hypothesized that the narrow column space concentrating a

higher level of energy and the large density variations throughout its anatomic layers subjected

the spinal cord to the large fluctuations of shear stresses.

82

Figure 5-5. Distributions of von-Mises stress of the brain were shown in the sagittal cross-sectional view for the

250g TNT ground blast-head simulation at different times from 1.6 ms to 2.1 ms

1.6 ms 1.7 ms 1.8 ms

1.9 ms 2.0 ms 2.1 ms

83

(a) (b)

(c) (d)

(e) (f)

Figure 5-6. The time histories of von-Mises stress recorded by various gauge points of the five ground blast-head

simulations: (a) No. 3 on cortex at SSS, (b) No. 6 on the frontal cortex, (c) No. 14 on the occipital cortex, (d) No. 19

on the lower brainstem, (e) No. 21 on the hypothalamus, (f) No. 22 on the right temporal cortex

84

The time histories of von-Mises stresses predicted at the cortex at SSS, frontal cortex,

occipital cortex, lower brainstem, hypothalamus, and right temporal cortex are shown in Figure

5-6. The von-Mises stresses of the central parenchyma were less than 0.1 kPa for all the

simulations, and therefore were not shown here. At any location in the brain, with the increase in

the explosive mass from 250g TNT to 450g TNT, the pattern of von-Mises stresses stayed the

same, while the peak value of the von-Mises stresses increased and occurred earlier. This

phenomenon was similar to the relationship between the pressure responses of the brain and the

blast intensity.

Although the shear stresses did not show an "impulse" pattern of the intracranial pressure,

they still increased largely in the beginning stage. The von-Mises stresses at most cerebral sites

except for the hypothalamus did not reach the peak magnitudes early (before 1.8 ms) in the blast

wave-head interactions for all the five simulation cases. Figure 5-6 shows that the peak von-

Mises stresses in the cortex at the SSS, frontal cortex, occipital cortex, lower brainstem, and right

temporal cortex occurred after 1.8 ms, when the primary pressure waves had already passed

these locations. This delay between the peak von-Mises stresses and peak intracranial pressures

can be attributed to the time lag effect of brain viscoelasticity. Moreover, after the peak

magnitudes occurred, the von-Mises stress maintained a high level. This is quite different from

the “impulse” pattern of the intracranial pressures. Taking the 450g TNT simulation case as an

example, the von-Mises stress of the lower brainstem reached a peak magnitude of 0.62 kPa at

1.89 ms, while at 3.04 ms, the stress magnitude was 0.6 kPa, which was still considered high as

compared with the peak magnitude. The other example was that in the right temporal cortex, the

peak magnitude of von-Mises stress was 0.87 kPa occurring at 4.31 ms. Before 4.31 ms, the

highest stress magnitude was 0.63 kPa occurring at 1.87 ms. Therefore, it is thought that the

85

consistent high shear stresses at the gray matter-white matter junctions might reduce the

tolerance of neuron fiber tracks to shear stresses.

In the 450g TNT simulation case, the von-Mises stresses in the frontal cortex, lower

brainstem, and the right temporal cortex were higher than 0.6 kPa. Among the locations proximal

to blast, the hypothalamus had the lowest von-Mises stress 0.17 kPa, which was also the lowest

von-Mises peak value possessed by all the cerebral locations, as shown in Figure 5-6. At the

locations distal to blast, the cortex at the SSS and the occipital cortex had von-Mises stresses

lower than 0.5 kPa. Therefore, with the exception of the hypothalamus, the von-Mises stresses

were higher at the locations proximal to blasts. The temporal cortexes were subjected to the

highest von-Mises stresses among all the cerebral locations in the 400g TNT and 450g TNT

cases. However, in the 250g, 300g, and 350g TNT cases, the highest von-Mises stresses occurred

in the frontal cortex instead of the temporal cortexes. The left temporal cortex had high shear

stresses equivalent to the right temporal cortex, and therefore only the information of the right

lateral temporal cortex was explicitly shown here.

Table 5-2 summarizes the peak von-Mises stresses at the frontal cortex, occipital cortex,

and the right temporal cortex for all simulation cases. From Table 5-2, it is observed that the

highest von-Mises stress of the brain in the ground-blast simulations was 0.87 kPa, which was

much lower than that of the horizontal simulations. Therefore the cerebral von-Mises stresses in

the ground blast-head simulations were far below the axonal injury criterion proposed by Zhang

et al. (2004). This again supported the hypothesis that shear stress might not be the main injury

causation of blast TBI as opposed to intracranial pressure. However, the positive correlation

between the TNT mass and the shear stress at every cerebral location implies that once the TNT

86

mass exceeded a certain amount, the shear stress of brain could exceed the injury criterion and

cause DAI injury.

Table 5-2. Peak von-Mises stresses in kPa at frontal cortex (gauge No. 6), occipital cortex (gauge No. 14), right

temporal cortex (No. 22) of the five simulations cases

Location/gauge number TNT mass

250g 300g 350g 400g 450g

Frontal cortex/No. 6 0.59 0.66 0.71 0.79 0.83

Occipital cortex/No. 14 0.27 0.28 0.30 0.32 0.33

Right temporal cortex/No. 22 0.47 0.56 0.67 0.80 0.87

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6.0 BLAST-HEAD INTERACTION SIMULATIONS OF EXPOSURE TO BLAST IN

A SMALL ROOM

In this chapter, a computational scheme was developed to determine the propagation patterns of

the blast waves generated in a small room, which has complex wave reflections. This scheme

was to simulate the scenario of a blast wave detonated in the space of a small room with one wall

opened to the street battle. The charges of the detonated TNT in the small room were still 250g,

300g, 350g, 400g, and 450g as used in the foregoing two blast-head simulation scenarios. The

mechanical responses of human head to the complex blast waves were analyzed to evaluate the

brain injury severities and the correlations between the blast waves and the potential injuries.

The von-Mises stresses of the brain were analyzed as well.

6.1 PREPROCESSING OF SIMULATIONS

The dimension, mesh, and material properties of the room model were modeled as a 3D air space

by using the methods described earlier in the section 3.3. This simulation scenario consisted of

five blast-head simulations which also used the 250g, 300g, 350g, 400g, and 450g TNT spherical

charges. The FE head model was placed one meter away from the anterior surface of the room

space and was at the center of the X-Z plane in which it was located. The head model faced to

the 3D blast waves which were located at the anterior surface of the room space. Therefore, the

88

location and orientation of the FE head model, along with the blast settings and locations were

completely identical to that of the anterior blast-head simulations.

Except for the anterior wall, all five other room walls were given closed boundary

conditions which acoustically performed like rigid walls of a room. The anterior room surface

was assigned an open boundary condition in order for the blast energy in the 3D space to be

partially released, since a perfectly sealed room space was not realistic in real battle field. The

boundary condition settings of the room space made it equivalent to a partially enclosed small

room. Figure 6-1 shows the computational schematic of a 3D air blast within the Euler-FCT

model of the small room.

An air gauge point (No. 24) was placed in the 3D space in front of the human face. And

the other air gauge point (No. 25) was placed in the space behind the human head in order to

track the time histories of the reflected blast waves impinging on the back of the head model

(Figure 6-1). The locations of the twenty-three gauge points in the FE head model were kept the

same as that in the simulations of horizontal blast exposures in order to comparatively quantify

the intracranial pressure levels which were reinforced by the wall reflections. The bottom of the

neck was not assigned any constraint, consistent with the foregoing simulation scenarios. The

duration of every room blast-head simulation was set to 10 milliseconds because the reflected

blast waves needed more time than the foregoing simulations to be fully completed.

89

Figure 6-1. Computational schematic of 3D air blast within the small room which was assigned with open boundary

condition (B.C.) at the anterior surface

90

6.2 BRAIN PRESSURE RESPONSE TO BLAST IN A SMALL ROOM

The five space surfaces assigned with closed boundary conditions reflected any blast wave

incident upon them. The time-lapse contours of the blast waves moving in the room space at

2.0ms, 3.0 ms, 4.0 ms, 4.5 ms, 5.0 ms, and at 8.0 ms were shown in Figure 6-2. Figure 6-3 shows

the time histories of the atmospheric pressures at the front space (gauge No. 24) and at the rear

space (gauge No. 25) of the head model. It is observed that the wall reflections greatly affected

the patterns of blast waves, and therefore very complex blast waves moving within the room

space were formed. The reflected blast waves made this blast-head simulations scenario quite

different with the foregoing ones.

Before impinging on the walls, the initial blast wave propagated the same as in the

anterior blast-head simulations. Therefore, the peak pressures of the initial blast waves were the

same as those observed in the anterior blast-head simulations (Figure 6-3a). Once the initial blast

wave reached the walls, they were reflected and then propagated in new directions (Figure 6-2).

The top wall, the bottom wall, the left lateral wall, and right lateral wall reflected the initial blast

waves at 0.95 ms, and formed four symmetrical blast waves propagating toward the posterior

wall obliquely, as shown in the 2.0 ms and 3.0 ms pictures in Figure 6-2. The initial blast wave

reached the posterior wall at 1.65 ms, and formed a horizontal blast wave propagating toward the

anterior wall. The new horizontal wave impacted on the back side of the head model around 3.0

ms, and therefore was indicated by the second wave crest shown in Figure 6-3b.

91

Figure 6-2. Time-lapse contours of a blast wave propagating within the room at 2.0 ms, 3.0 ms, 4.0 ms, 4.5 ms, 5.0

ms and at 8.0 ms for the 250g TNT room blast-head simulation

2.0 ms 3.0 ms 4.0 ms

4.5 ms 5.0 ms 8.0 ms

92

(a)

(b)

Figure 6-3. Atmospheric pressure time histories tracked by (a) the air gauge point No. 24 in the frontal space of the

head model, (b) the air gauge point No. 25 in the rear space of the head model

93

The four oblique reflected blast waves interacted with the horizontal reflected blast waves

as shown in the pictures at 3.0 ms, 4.0 ms, and 4.5 ms in Figure 6-3. Since the energy of the four

oblique reflected waves was higher than that of the horizontally reflected waves, the interaction

formed a new blast wave propagating toward the posterior wall. This new blast wave impacted

the face of the head model around 5.0 ms, as shown by the 5.0 ms picture in Figure 6-2. This is

also revealed by the second blast wave crest in Figure 6-3a. After 5.0 ms, the four oblique waves

were reflected by the posterior wall and formed two strong blast waves impacting on the back

side of the head model, as shown by the third and the fourth blast wave crests in Figure 6-3b.

The fourth wave crest recorded by gauge No. 25 had the peak positive pressures ranging from

213 kPa to 318 kPa, which was the highest level among all the blast wave crests passing through

the rear space of the head model. After the major energy of the blast waves in the room had

dissipated from the anterior surface of the room space, the final reflected blast wave impacted on

the head model 8.0 ms, as shown in the 8.0 ms picture in Figure 6-2.

Figure 6-4 shows the pressure-time histories recorded by various intracranial gauge

points. As expected, the initial blast wave and the reflected blast waves impacting on the head

model resulted in a variety of pressure waves in the head model. For all of the intracranial

locations, the initial crests of the intracranial waves were identical to those in the anterior blast-

head simulations because the mechanical responses of the head model were identical to that in

the anterior blast-head simulations before the reflected waves impacted on the head model.

Around 3.0 ms, the intracranial waves exhibited a second crest which was caused by the

reflected blast wave shown in the 3.0 ms picture in Figure 6-2. However, the second intracranial

wave-crest was insignificant in the frontal cortex as compared to the other locations. Around 5.0

ms, the intracranial locations experienced their highest or the second highest wave crests, which

94

were induced by the reflected blast waves impacting on the face of the head horizontally at 5.0

ms, as shown in the 5.0 ms picture of Figure 6-2. Around 6.5 ms, the occipital cortex, the

posterior margin of the tentorium cerebelli, the lower brainstem, and the right temporal cortex

experienced significant wave crests, which were caused by the fourth crest of the blast waves,

shown in Figure 6-3b, impacting on the rear side of the head model.

In the CSF at the SSS, frontal cortex, and lower brainstem, the peak positive pressures

were achieved by the initial crests of the intracranial pressure waves formed by the initial, direct

blast waveform for all the five cases. In the occipital cortex, the peak positive pressures for the

350g TNT and 400g TNT cases were created by the reflected blast waves; while for the 250g

TNT, 300g TNT, and 450g TNT cases, the initial crests of the intracranial pressure waves

created the peak positive pressures. In the posterior margin of the tentorium cerebelli, all the

cases except the 450g case achieved the peak positive intracranial pressures from the reflected

blast waves. In the left and right temporal cortexes, all the cases except the 250g case achieved

the peak positive pressures from the initial blast wave. Therefore, the blast waves reflected by

the room did increase the peak intracranial pressures at some cerebral locations.

95

(a) (b)

(c) (d)

(e) (f)

Figure 6-4. Pressure-time histories recorded by various gauge points for the room blast-head simulations: (a) No. 2

in CSF at SSS, (b) No. 6 in the frontal cortex, (c) No. 14 in the occipital cortex, (d) No. 18 at the posterior margin of

the tentorium cerebelli, (e) No. 19 on the lower brainstem, (f) No. 22 on the right temporal cortex

96

Figure 6-5. Pressure distributions of the brain in the 400g TNT room blast-head simulation from 4.5 ms to 5.0 ms

4.5 ms 4.6 ms 4.7 ms

4.8 ms 4.9 ms 5.0 ms

97

For the 450g TNT case, the occipital cortex achieved a peak negative pressure of -96 kPa

at 7.1 ms; and the posterior margin of the tentorium cerebelli achieved a peak negative pressure

of -99 kPa at 7.4 ms. Compared with the corresponding peak positive pressures, the magnitudes

of these peak negative pressure were still at high levels. Since they were caused by the reflected

blast waves impinging on the back of the head and were lower than the peak negative pressures

obtained from the initial blast waves, the conclusion that the reflected blast waves could increase

the peak intracranial pressures was validated. As discussed above, the sharp transitions from the

high positive pressures (compression) to the high negative pressures (tension) at the same

cerebral locations might bring additional damage to the brain. Sharper transitions from

compression to tension were observed for the room blasts. Therefore, the room blast scenarios

are also speculated to have higher potential to create damage than the open-field blast scenarios.

The time-lapse pressure distributions of the 400g TNT room blast-head simulation from

4.5 ms to 5.0 ms are shown in Figure 6-5, from which it is clearly observed that the intracranial

pressure waves propagated from the frontal part to the rear part of the brain. The intracranial

pressure waves during this time range were produced by the strongest reflected blast wave.

Contusion occurrences and severities at several cerebral locations were againevaluated by

using the same index suggested by Ward et al. (1980), and are summarized in Table 6-1 and

Figure 6-6. The prediction of contusion injury severities at the SSS cortex, frontal cortex,

temporal cortexes, hypothalamus, and lower brainstem were identical to that of the anterior blast-

head simulations. The only exception was the occipital cortex, which had a minor contusion in

the 350g TNT case, but it had no injury in any other anterior blast-head simulation. The minor

contusion in the occipital cortex for the 350g TNT case was induced by the strongest reflected

blast wave impacting the head at 4.5 ms.

98

Table 6-1. Predicted contusion injury severities at typical cerebral sites with respect to impinging BOPs at the blast

incident side in the room blast-head simulations

Peak BOP

(TNT weight)

Cortex

at SSS

Frontal

cortex

Occipital

cortex

Temporal

cortexes

Hypothalamus Lower

Brainstem

291 kPa (250g) None None None None None None

321 kPa (300g) Minor Minor None None None None

349 kPa (350g) Minor Minor Minor None Minor Minor

379 kPa (400g) Serious Serious None Minor Minor Minor

413 kPa (450g) Serious Serious None Minor Serious Minor

Figure 6-6. Predicted contusion injury location and severity of the room blast-head simulations

ICP 235 kPa - Serious Contusion

ICP 173 kPa - Minor Contusion

BOP 291 kPa

BOP 321 kPa

BOP 349 kPa

BOP 379 kPa

BOP 413 kPa

Temporal cortexes:Minor contusions for BOP 379 kPa and 413 kPa

99

6.3 BRAIN SHEAR STRESS RESPONSE TO BLAST IN A SMALL ROOM

The analysis of the brain shear stress response to the room blasts was based on the von-Mises

stresses of the brain as in the foregoing chapters. The time-lapse distributions of the cerebral

von-Mises stresses in the sagittal cross-sectional view for the 400g TNT ground blast-head

simulation were depicted in Figure 6-7 at different times ranging from 4.5 ms to 5.0 ms with 0.1

ms interval as the counterpart of the pressure distributions shown in Figure 6-5. Similar to the

horizontal blast-head simulations and the ground blast-head simulations, the high shear stresses

mainly occurred at the brain surfaces which were adjacent to the CSF, while the central

parenchyma were subjected to comparatively low von-Mises stresses which were less than 0.15

kPa in all the five room blast-head simulations.

100

Figure 6-7. Distributions of von-Mises stress in the sagittal cross-sectional view of the brain for the 400g TNT

room blast-head simulation at different times from 4.5 ms to 5.0 ms

4.5 ms 4.6 ms 4.7 ms

4.8 ms 4.9 ms 5.0 ms

101

The time histories of the von-Mises stresses predicted at the cortex at the SSS, frontal

cortex, occipital cortex, lower brainstem, hypothalamus, and right temporal cortex are shown in

Figure 6-8. The time histories of the von-Mises stresses in the central parenchyma are not shown

here because they were several orders of magnitude lower than that at the brain surface. Figure

6-8 shows that most of the cerebral locations experienced fluctuations of high von-Mises stresses.

Before the reflected blast waves impacted the head model, the von-Mises stresses of the brain

were identical to that of the anterior blast-head simulations. At the same cerebral location, the

patterns of the von-Mises stresses for the simulations were similar but still had differences for

the five levels of blast. At the hypothalamus, the patterns of the von-Mises stresses for the

simulations remained the same during the whole 10 ms, while the peak von-Mises stress

increased and occurred earlier as the explosive mass increased. However, in the cortex at the SSS,

frontal cortex, occipital cortex, lower brainstem, and right temporal cortex, each of the patterns

for the von-Mises stresses remained the same before 4 ms for each site, and varied thereafter,

exhibiting the influence of the reflected blast waves. This phenomenon was similar to that

observed for the pressure responses of the brain.

102

(a) (b)

(c) (d)

(e) (f)

Figure 6-8. The time histories of von-Mises stress recorded by various gauge points for the room blast-head

simulations with five amounts of TNT: (a) No. 3 on cortex at SSS, (b) No. 6 on the frontal cortex, (c) No. 14 on the

occipital cortex, (d) No. 19 on the lower brainstem, (e) No. 21 on the hypothalamus, (f) No. 22 on the right temporal

cortex

103

In the cortex at the SSS, the 450g TNT simulation case had the highest von-Mises stress

after 4 ms, while the other four cases achieved the highest von-Mises stresses before 4 ms. In the

frontal cortex, except the 300g TNT case, the other four cases had the highest von-Mises stresses

before 1 ms. In the occipital cortex, all the five simulation cases achieved the highest von-Mises

stresses around 7.0 ms, and the 350g TNT case had the highest von-Mises stress. In the lower

brainstem, except the 300g TNT case, the other four cases had the highest von-Mises stresses

before 4 ms. In the temporal cortexes, the highest von-Mises stresses of all the five simulation

cases happened after 4 ms. Therefore, there was not a clear rule that governed the time of

occurrence of the highest von-Mises stresses in the brain for the room blast scenario because the

magnitudes of the von-Mises stresses at any cerebral location were affected by the intensities of

the reflected blast waves impacting on the head model. Hence, the occurence times of the highest

von-Mises stresses at a cerebral location could indicate the intensity differences between the

initial blast wave and the reflected waves impacting on the adjacent area of this location.

The maximum von-Mises stress of all the room blast-head simulations occured at the

lower brainstem for the 450g TNT case, with the same value (2.81 kPa) as that of the anterior

blast-head simulations. According to the axonal injury criterion proposed by Zhang et al. (2004),

the room blast-head simulations did not obtain any DAI lesions. This indicated that shear stress

might not be the main injury causation of blast TBI as opposed to intracranial pressure in the

room blast scenario, even though the reflected blast waves enhanced the level of shear stresses at

some of the cerebral locations. While the consistent fluctuations of high level shear stresses

might reduce the tolerance of the brain tissue to shear stress. Therefore, a DAI injury criterion

including both the shear stress magnitude and the fluctuation of high shear stress should be

addressed in future research.

104

7.0 FINITE ELEMENT ANALYSIS OF SUBDURAL HEMORRHAGE

Subdural hemorrhage/hematoma is the bleeding caused by BV damage or rupture within the

subdural space (Gennarelli and Thibault 1982, Yamashima and Friede 1984). Subdural

hemorrhage is one of the leading injury types of traumatic brain injury. In order to assess the

occurrence and injury severity of subdural hemorrhage for the blast-head simulations conducted

in the foregoing context, mechanical properties of BV were estimated by fitting experimental

inflation results of a BV sample to a selected anisotropic hyperelastic constitutive model, and the

finite element analysis (FEA) of BV rupture was performed by using the internal pressure

loadings identical to the CSF pressures at SSS of the anterior blast-head simulations, which had

the highest CSF pressures at the SSS among all the blast-head simulations. For every explosive

mass, the highest CSF pressure at SSS in the anterior blast-head simulations and that in the room

blast-head simulations were the same, therefore, this chapter conducted the FEA of subdural

hemorrhage based solely on the results of the anterior blast-head simulations.

7.1 MECHANICAL TESTING OF HUMAN BRIDGING VEIN

Although some results of the mechanical experiments on human bridging vein were published

recently (Pang et al. 2001, Monson et al. 2005), it was impossible to fit these experimental data

to the hyperelastic constitutive models which were able to represent the 3D constitutive relations

105

between stress and strain. Hence, a standard inflation experiment for blood vessels was devised

to generate suitable experimental data which could be used for curve fitting the measured

mechanical properties of human bridging vein.

Three human bridging veins were harvested at autopsy. The bridging vein (BV)

segments were catheterized (polyethylene venous catheter) after opening the superior sagittal

sinus, and were maintained at in-vivo length with the microvascular clamps against the catheter.

After the excision, the clamped vein samples and catheters were transported to the testing

laboratory in containers with phosphate buffered saline (PBS) solution. The BV surrounding

tissues were cleaned before mounting the BV samples onto the perfusion cannulae of the

inflation-extension biomechanical testing system (Santelices et al. 2007, VanEpps et al. 2009)

equipped with a non-contacting laser micrometer (Beta LaserMike, Dayton, OH). One intact BV

sample maintained its integrity for the full testing. Figure 7-1 shows an intact human bridging

vein was mounted in the inflation-extension vascular testing system before the onset of the

inflation test. The BV segment was bathed in water and was kept at its in-vivo longitudinal

stretch after pre-measuring the in vivo length of the BV segment. The structure of BV was

extremely soft, therefore the shape of its cross section was deformed remarkably due to the lack

of internal pressure after excision, therefore, the equilibrium state between the internal and

external hydraulic pressures of BV was achieved by the adjustment of pre-perfusion such that the

zero-load-state outer diameter of the BV could be accurately measured. The zero-load-state outer

diameter of the BV was measured to be 2.027 mm by the laser micrometer. The inner diameter

was 1.76 mm, as estimated from the average ratio of the wall thickness versus outer diameter of

BVs in Monson et al. (2005).

106

Before the inflation test, ten preconditioning cycles were carried out on the BV section to

eliminate the tissue-softening effects. After the preconditioning, the pressure-radius (P-r) curve

was obtained by inflating the vessel segment across a range of pressures from 0-20 mm Hg (0-

2.67 kPa) at the constant rate of 0.5 0.1 mm Hg/s (66.6 13.3 Pa/s). During the inflation, the

increasing BV external diameter was measured by the laser micrometer. The corresponding

inflating pressure was measured by a pressure sensor (TruWave transducer, Edwards lifesciences,

Irvine, CA). The measured data of the changing diameter versus the corresponding inflation

pressure were recorded by a PC-based data acquisition system. This data was then processed and

was used for the following work of characterizing the mechanical properties of bridging vein in a

selected anisotropic hyperelastic constitutive model. Ideally, multiple specimens would be tested

and averaged, however additional samples were not available. Nonetheless, a method of fitting

data from any future experiments has been devised.

Figure 7-1. Human bridging vein mounted in the inflation-extension vascular testing system (Wang et al. 2012)

107

7.2 CONSTITUTIVE MODELING AND MATERIAL CURVE FITTING OF

BRIDGING VEIN

The elastin/ground matrix and collagen fibers are the two major structures bearing the

mechanical loadings in blood vessels, which also contain smooth muscle cells. Compared to

arteries, veins have thinner vessel walls, higher contents of collagenous fibers, and lower

contents of smooth muscle cells (Rezakhaniha and Stergiopulos 2008). Consistent research

efforts in academia have been put into developing accurate constitutive models to numerically

describe the nonlinear phenomenon exhibited in the loading processes of blood vessels.

Strain energy function (SEF) per unit volume is the preferred method to characterize the

nonlinear mechanical properties of vascular tissue. Using the SEF for blood vessels, the

constitutive relations can be derived from the SEF. Furthermore, the Cauchy stress and tangent

stiffness matrix can be derived from the SEF in order to implement the user-defined material

subroutine in a commercial finite element analysis package (Gasser et al. 2006, Sun et al. 2008,

Li et al. 2012).

Early SEF frameworks for biological soft tissues are purely phenomenon-based functions,

such as the well-known Fung constitutive model (Fung et al. 1979), which is a mathematical

function bearing little physiological meaning. Lately, a structure based or perhaps constituent

based SEF for arteries was proposed by Holzapfel et al. (2000) to characterize the passive

structural responses of the non-collagenous matrix and the collagen fibers. This model treats the

non-collagenous material as an isotropic ground matrix, which is reinforced by two families of

anisotropic frameworks of collagen fibers. The advantage of this constitutive model over the

phenomenon-based SEFs is its ability to completely describe the 3D stress and strain relationship

of vascular tissues, and thus a more accurate finite element implementation can be realized.

108

Based on the classic theories of the fiber-reinforced finite elasticity, the Holzapfel-Gasser-Ogden

model has been widely recognized in the active biomechanical research of blood vessels. In the

present study, this SEF was adopted for the constitutive modeling of human bridging vein, which

is constituted mainly by elastin and collagen. As mentioned above, veins contains less smooth

muscle cells than arteries, thus even more striking, the Holzapfel-Gasser-Ogden model is

naturally more suitable for the constitutive modeling of vein than the arterial modeling which

was initially developed by Holzapfel et al. (2000).

The Holzapfel-Gasser-Ogden model was adopted for the mechanical characterization of

human bridging veins in the present study. The strain energy of the bridging vein was constituted

by a part Wiso associated with isotropic finite deformations and a part Waniso associated with

anisotropic finite deformations. Wiso, the isotropic part of the overall response of the vessel tissue,

represented the non-collagenous matrix in the form

( )

(7.1)

Waniso, the anisotropic part of the overall SEF of vessel wall, arising only from the

anisotropic finite deformations of the two families of collagen fibers, had the form

∑{ [ ( ) ] }

(7.2)

Hence, the complete strain energy function is given by

( )

∑{ [ ( ) ] }

(7.3)

where c, k1, and k2 were the effective material parameters. The variables c and k1 had dimensions

of stress, and k2 was dimensionless. I1 is the first principal invariant of the right Cauchy-Green

deformation tensor derived from the deformation tensor of the vascular material. The

109

orientations of the two families of collagen fibers were defined by the two unit vectors a1 and a2

respectively. I4 and I6 denoted the squares of the collagen stretches in the directions of a1 and a2,

respectively. I4 and I6 had the final derived forms in terms of the two independent stretches and

z, and the mean fiber angle β:

(7.4)

where was the radial stretch, z was the axial stretch. The mean fiber angle β was assigned to

be 29 for the directions of both unit vectors. The value of β was obtained directly from the value

of the collagenous fiber angle of arterial media by Holzapfel et al. (2000) because experimentally

detecting the fiber angle of BV was too hard to be performed using the traditional measuring

methods such as optical microscopy (Nierenberger et al. 2012).

The determination of the material parameters in the constitutive model used the

experimental data obtained using the processes described in section 7.1 above. A pressure versus

radius (P-r) curve was generated using the data produced by the conducted pressure-inflation test

on the human bridging vein section. To derive the analytical solution of the pressure versus

radius relationship corresponding to the vascular inflation test, Cauchy's equation of equilibrium

was adopted in the form

(7.5)

where div () represented the spatial divergence of tensor field (), and was the Cauchy stress.

In the absence of body forces b, equation (7.5) had the self-equilibrated form

(7.6)

In cylindrical coordinates (r, , z), because of the symmetry, equation (7.6) had only the

normal stresses rr, , zz which were the principal stresses. Thus, equation (7.6) consisted of

just the radial equation

110

( )

(7.7)

The conducted inflation test involved the homogeneous pressure P applied to the internal

surface of the bridging vein segment with closed ends. Therefore the boundary conditions of the

bridging vein were rr = -P for r = a and rr = 0 for r = b, where a was the inner radius, and b

was the outer radius. Using the above boundary conditions, integration of equation (7.7) led to

the forms

∫ ( )

(7.8)

⁄ (7.9)

where a and b were the values of at r = a and r = b. The detailed derivations of equation (7.8)

can be found in Ogden (2009). The present study considered the bridging vein segment as a thin-

walled tube. Following the derivations in Holzapfel and Ogden (2010), equation (7.8) was

approximated to be

(7.10)

where was the ratio of the vessel wall thickness to the internal radius in the unloaded

configuration. The bridging vein segment was kept at its in-vivo length in the present inflation

test, so the axial stretch was 1 in equation (7.10), which provided the necessary analytical

equation/relationship of pressure versus circumferential stretch of bridging vein.

The raw experimental data (P-r data) of the conducted inflation test was processed into

the form of pressure versus circumferential stretch (P- data). With the analytical function for

this processed experimental data, the values of the material parameters in the form of Holzapfel-

Gasser-Ogden model could be obtained using curve fitting methods.

111

Figure 7-2. Experimental data and analytical solution from fitted material parameters

A modified Levenberg-Marquardt method was used to fit the analytical equation of

pressure versus stretch to the P- data set. The parameters obtained for equation (7.3) were: c =

1.203 kPa, k1 = 0.725 kPa, k2 = 87.88. Table 7-1 summarizes the material parameters of the

Holzapfel-Gasser-Ogden model for the tested human bridging vein. The fitted material

parameters were adopted in the following finite element analysis of bridging vein.

Table 7-1. Material parameters of human bridging vein

C (kPa) k1 (kPa) k2 (dimensionless) Β (deg)

1.203 0.725 87.88 29

112

7.3 INJURY PREDICTION OF SUBDURAL HEMORRHAGE

Specific assumptions were made for the finite element analysis (FEA) of the human bridging

vein. First, since the bridging vein connects the superior sagittal sinus and the brain, the effective

length of the bridging vein FE model involved in the mechanical responses of the superior

sagittal sinus was assumed to be the CSF layer thickness from the skull to the brain at the SSS in

the adopted finite element human head model. Therefore the effective length of the bridging vein

segment for simulation was determined to be 6.5 mm. The kinematics of human head model in

all the foregoing blast-head simulations revealed that there was no skull-brain relative

displacement at all for all of the blast-head interaction simulatinos. Therefore, just the blast-

induced peak CSF pressures at SSS were considered to be the mechanical cause of bridging vein

damage/rupture.

Note that the simulations of the anterior blast exposures had the highest peak pressure

levels in the CSF at the SSS among all the three simulation sets of the horizontal blast-head

simulations. Also, the peak CSF pressures at the SSS of the anterior blast-head simulations were

identical to that of the room blast-head simulations. Therefore, the maximum positive CSF

pressure at the SSS region in each of the five anterior blast-head simulations was assigned to be

the intraluminal pressure loading on the bridging vein finite element model. For each of the

anterior blast-head simulations, one bridging vein finite element simulation was performed using

the respective peak CSF pressure recorded by the gauge No. 2 at SSS (Figure 4-3b). The cross-

sectional dimension of the bridging vein model was modeled to be the same as that of the

bridging vein segment in the inflation test. The length of the bridging vein finite element model

was its effective length, 6.5 mm. The two end surfaces of every bridging vein finite element

model were assigned with displacement-fixed boundary conditions. Since the bridging vein was

113

modeled as a pure cylindrical shell, axis-symmetry was used to simplify the finite element

modeling, i.e., only 1/4 of the bridging vein was modeled. The axial yield stress ( Y = 1.15 MPa)

and the axial ultimate stress ( U = 1.32 MPa) of human bridging veins were estimated from the

BV failure experiments using uniaxial stretching (Monson et al. 2005). Because Monson et al.

(2005) stretched the bridging vein samples purely along the cylindrical axis, the vein ultimate

stress they found was used as the rupture criteria against the maximum axial Cauchy stress for

each of the bridging vein simulations.

Figure 7-3 shows the axial Cauchy stress of the bridging vein finite element analysis

corresponding to each of the five impinging BOPs at the blast incident side. Because the axial

Cauchy stress from the BV simulations of 291 kPa and 321 kPa BOPs were below the yield

stress of the BV, a blast victim was not predicted to be at a great risk of suffering a subdural

hemorrhage by these blast levels. In the BV simulation of 349 kPa BOP, the maximum axial

Cauchy stress was 1.24 MPa (Figure 7-3), which exceeded the yield stress of bridging veins

instead of the ultimate stress. In the BV simulation of 379 kPa BOP, the maximum axial Cauchy

stress was just above the ultimate stress of bridging veins. Hence it was concluded that as long as

the impinging BOP at the blast incident side exceeded 379 kPa, the bridging vein would

definitely rupture.

114

(a) (b)

(c) (d)

(e)

Figure 7-3. Axial Cauchy stress of the bridging vein finite element analysis corresponding to impinging BOP at the

blast incident side: (a) 291 kPa, (b) 321 kPa, (c) 349 kPa, (d) 379 kPa, (e) 413 kPa

115

Although the axial Cauchy stresses which had the maximum value between the yield

stress and ultimate stress did not necessarily indicate the occurrences of bridging vein ruptures,

yielding of blood vessels could involve fiber failures, which might lead to a later onset of

vascular injury. Therefore, the prediction of bridging vein rupture in the present study was based

on the criterion of bridging vein yielding. In sum, subdural hemorrhage was predicted to occur

once the impinging BOP at the blast incident side exceeded 349 kPa. In other words, a peak

blast-induced CSF pressure at the SSS above 220 kPa was estimated to lead to subdural

hemorrhage. The impinging BOP at the blast incident side, the respective CSF pressure at the

SSS, the induced respective maximum axial Cauchy stress of the bridging vein, and the bridging

vein failure prediction for each of the five cases of anterior blast exposure are summarized in

Table 7-2.

Table 7-2. Peak pressure tracked by the gauge No. 2 in the CSF at SSS, and the respective maximum axial Cauchy

stress and failure prediction of the BV with respect to the impinging BOP at the blast incident side

Peak BOP

(TNT weight)

Peak Pressure of

Gauge No. 2

BV Maximum Axial

Cauchy Stress (MPa)

Failure

Prediction

291 kPa (250g) 175 kPa 0.95 No

321 kPa (300g) 202 kPa 1.11 No

349 kPa (350g) 220 kPa 1.24 Yes

379 kPa (400g) 241 kPa 1.33 Yes

413 kPa (450g) 270 kPa 1.50 Yes

116

8.0 CONCLUSIONS AND DISCUSSIONS

In the present study, a full human head FE model and a numerical blast domain model were

created. Three scenarios of blast wave-head interaction simulations were conducted to reproduce

the human head exposures to horizontal blast waves from three principal directions, to the

ground blasts, and to the blast waves within a room. Five blast-head computer simulations of

250g, 300g, 350g, 400g, and 450g TNT charges at one meter distance were conducted for each

of the three scenarios.

In the blast-head simulation scenario involving the horizontal anterior, right lateral, and

posterior blast exposures, the sensitivities of the intracranial mechanical responses to blast

intensities and exposure orientations were studied. The time-lapse pressure distribution of the

brain revealed that the intracranial pressure wave propagated from the proximal blast side to the

distal side for any blast orientation. At most of the cerebral locations, the pressure-time histories

had an “impulse-like” pattern, which was very obvious at the proximal cerebral sites to the

blasts. During the process of intracranial wave propagation from the proximal side to the distal

side, attenuation of the pressure amplitude was observed, and the highest pressure levels were

found to be at the parts of the brain that were proximal to blast for any blast orientation. On both

the proximal side and distal side of the brain exposed to blasts, the positive pressures were much

more significant than the negative pressures. The main peak positive pressure and the subsequent

peak negative pressure occurred over a very short period of time which was less than 0.8 ms.

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This sudden transition from high-level compression to tension might introduce an additional

mechanism of axonal injury. This hypothesis also agrees with that was proposed by Taylor and

Ford (2009).

The intracranial pressure pattern at the blast proximal site and distal site predicted by the

present study was quite different with the "coup and contrecoup" intracranial pressure pattern

observed for a human head sustaining impact or acceleration loadings. It is concluded that the

direct blast wave propagation into the brain instead of the blast-induced impact generated the

propagating intracranial pressure wave. This conclusion was similar to that described in the

literature (Moore et al. 2009, Taylor and Ford 2009, Nyein et al. 2010), which excluded the

“coup and contrecoup” pattern from the intracranial pressure patterns of bTBI too. But they did

not analyze the pressure changes along the pathway of the propagating intracranial wave as we

did. We discovered that absorption in the cerebral tissue resulted in decreasing intracranial

pressures from the peak at the proximal side of the head along the path of propagation through

the brain until the pressure levels were enhanced by the wave concentration effects of the narrow

occipital region. The distribution pattern of the blast-induced intracranial pressure is still

controversial. Chafi et al. (2009) predicted that the alternating compression and tension occurred

at both of the coup and contrecoup sites due to the brain translational and rotational movement

which might be attributed to the blast-induced impact. Ganpule et al. (2012) predicted that the

typical “coup and contrecoup” pattern occurred at the blast proximal site and the distal site, and

that highest positive pressure occurred at the inner parenchyma instead of the proximal cerebral

site.

The pressure levels in the cortex were at the side proximal to the blast and the highest

levels were found to be due to the lateral blast exposure as compared to the frontal and posterior

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blast exposures, indicating that the highest risk in suffering serious cortical injury was obtained

by the exposures to the side blast waves. The same conclusion was also derived by Taylor and

Ford (2009), who only simulated one blast level of the blast wave with 1.3 MPa peak pressure.

The other two references (Moore et al. 2009, Nyein et al. 2010) having the same conclusion with

us on the distribution pattern of the blast-induced intracranial pressure, did not investigate the

brain responses to the three blast exposure orientations. To our knowledge, the present study is

the only one including the human head responses to more than three blast levels for the anterior,

right lateral, posterior blast exposure orientations.

It was discovered that the pressure wave invariably traveled into the posterior fossa and

vertebral column contents, and caused high pressures in these regions, particularly the lower

brainstem and the spinal cord. Among all the fifteen horizontal blast-head simulations, the

highest intracranial pressure occurred in the lower brainstem of the posterior exposure. It is

found that the narrow regions, such as the foramen magnum, were able to concentrate the

pressure waves and thus to enhance the pressure levels there. Therefore, it is speculated that the

injury of the brainstem and the spinal cord caused by the pressure wave transmitted into the

posterior fossa and the foramen magnum might be one of the primary injury mechanisms of

bTBI. We have not found any literature containing a similar point of view on the injury pattern

of the brainstem in bTBI.

Besides the above findings on the pressure wave patterns of the brain responses to the

blast waves, it was also found that there was a higher possibility that serious cerebral contusion

could occur on the side of the brain that was proximal to the blast based on an intracranial

pressure injury index published by Ward, et al. (1980). The injury severities of the contusions at

several cerebral locations of the horizontal blast-head simulation scenario were predicted with

119

respect to the impinging BOPs at the blast incident side for each of the exposure orientations. For

all the simulation cases of the right lateral blast exposure, serious cortical contusions were

predicted to occur. The posterior blast exposure was predicted to be less harmful than the right

lateral blast exposure on the cortex, but to be the most harmful orientation to the brainstem,

which was predicted to have serious contusion in every simulation case of the posterior

orientation. The anterior blast exposure was the least harmful exposure orientation, for which the

291 kPa BOP at the blast incident side was the only case without injury among all the fifteen

simulation cases. Chafi et al. (2009) also used this pressure-based contusion criterion to predict

blast-induced contusion in their computational study, however, they did not predict specific

locations of contusions. To date, the summary of the cerebral contusion in bTBI in the present

study is the only one predicting the locations and the injury severities of the blast-induced

cerebral contusion with respect to the blast levels and the orientations.

In the evaluation of the shear stress responses of the human brain to the horizontal blast

waves, the von-Mises stresses at the lower brainstem and the spinal cord were predicted to be

higher than the other intracranial areas for all three blast orientations. The anterior blast exposure

was predicted to have the highest magnitude of von-Mises stress among the three orientations.

The von-Mises stresses on the cortex regions were found to be much larger than those inside the

brain. Despite that blast wave being propagated throughout the brain within 1 ms, the von-Mises

stresses of the brain still developed and kept high levels at several cerebral locations over the

whole simulation time. Similar to the present study, Taylor and Ford (2009) also predicted that

the gray-white matter junction and the inferior regions such as brainstem had high von-Mises

stresses and that the von-Mises stresses of the brain continued developing high levels through the

whole simulation time. By investigating the maximum shear stress, Chafi et al. (2009) predicted

120

that high shear stress was initially in the cortical region at the coup site, and then propagated to

other areas inside the brain, showing a different pattern than that of the present study. Chafi et al.

(2009) also found that the midbrain sustained a small amount of shear stress, which was in

agreement with the present study. Chafi et al. (2009) predicted that both the coup and contrecoup

sites had the highest shear stress, and that the axonal injury could occur. However, the present

study did not predict the highest shear stress at the contrecoup site. Moore et al. (2009) and

Ganpule et al. (2012) did not report the shear stress data.

Using the axonal injury tolerance level proposed by Zhang et al. (2004) based on the

magnitude of von-Mises shear stress, the present study predicted that shear stress-induced brain

injury would not occur under any circumstance of the present numerical simulations. Since both

high level pressures and shear stresses occurred on the brainstem or the spinal cord during the

blast events, future research attention should be addressed to the detailed injury mechanism of

the brainstem and the spinal cord in bTBI, i.e. to perform the microscopic biomechanical

analysis of the blast-induced injury there in order to evaluate the combinatorial effect of the

pressure impulse and high maintained shear stress.

To date, no other student was found with a similar computational study on the brain

responses to the ground blasts and the room blasts. In the simulation scenario of the human

exposures to the ground blasts, it was found that the reflections from the ground enhanced the

levels of the atmospheric blast waves generated from the same explosive charges as for the

horizontal blasts scenario. However, because the distance of the human head and the detonation

center for a standing person was longer than one meter, the resultant intracranial pressures and

von-Mises stresses were lower than that of the horizontal blasts simulation scenario. Similarly,

the cerebral regions that were proximal to the blast waves had higher peak pressures than the

121

distal regions. At the distal side of the brain including the parietal and occipital cortexes, the

peak positive pressures (compression) and the peak negative pressures (tension) took place

sequentially with equivalent magnitudes. This kind of compression to tension transition could

decrease the injury tolerance of the brain tissue to the high pressures. Similar to the horizontal

blast scenario, the high von-Mises stresses also prevailed on the brain surface regions which

were adjacent to the CSF. In contrast, the internal parenchyma had very low von-Mises stresses,

which were almost negligible. The von-Mises stresses also developed throughout the whole

simulation time. With even lower levels of the von-Mises stresses than that of the horizontal

blast scenario, it was predicted that the diffuse axonal injury would not occur in the ground blast-

head scenario.

In the simulation scenario where the human exposures were to blast waves traveling in a

room, it was predicted that the wall-reflected blast waves induced high level intracranial

pressures. At the posterior cerebral regions, the levels of the wave reflections-induced positive

pressures were even higher than the positive pressures induced by the initial blast waves.

Although the wave reflection-induced peak positive pressures at the other cerebral regions were

not predicted to be higher than those induced by the initial blast waves, the occurrence of more

high-pressure fluctuations in these regions was conjectured to decrease the brain tolerance to

contusion. Based only on the peak positive pressures, most of the cerebral regions had the same

contusion injury severity as for the anterior blast-head simulations, except the occipital cortex,

which had a peak positive pressure higher than the threshold of minor contusion for the 349 kPa

BOP case due to the reflected blast waves impinging on the back of head. The levels of the von-

Mises stresses were enhanced by the reflected blast waves in a number of cerebral regions, but

the diffuse axonal injury was still not predicted to appear.

122

The susceptibility to subdural hemorrhages, induced by human bridging vein failure as a

result of blast injury, was studied through finite element simulations on a vein submodel. In

every blast-head scenario, the relative skull-brain motion was predicted to be minimal (< 0.01

mm) in the primary blast loading events. High blast-induced intracranial pressures at SSS rather

than relative skull-brain motion (excessive shear stresses) were found to be the main injury

mechanism of blast-induced subdural hemorrhage. The outputs (CSF pressure at the SSS) of the

five blast-head simulations for the anterior blast exposure, possessing the highest level of CSF

pressure at the SSS among all the blast-head simulation scenarios, served as the loading

conditions for the separate finite element model of the bridging vein. Results from the BV finite

element analysis predicted that blast waves of 379 kPa impinging BOP at the blast incident side

in an open-space would lead to bridging vein rupture, since the resulting maximum axial Cauchy

stress exceeded the ultimate stress of the BV. Although the 349 kPa BOP case did not lead to a

complete BV rupture, the resultant maximum axial Cauchy stress reached the axial yield stress of

BV, suggesting an irreversible damage of the fibers of the BV. So, the yielding of the BV may

also lead to subdural hemorrhage. Therefore, a more conservative estimation of the injury

threshold of the blast subdural hemorrhage was 349 kPa BOP at the blast-incident side of the

human head.

Future improvements to the modeling are planned. Since the BV material constitutive

model is only based on one sample of BV, more BV samples will be tested for a better

estimation of material parameters. Experimental techniques to measure the zero-stress-state of

vessels and the longitudinal force (Jankowski et al. 2004) in the inflation test will be adopted to

get a more accurate estimation of the BV mechanical properties. In addition, more geometric

details can be added to the head model such as the falx and tentorium cerebelli, and the

123

separation of white matter, gray matter, cerebellum, and brainstem. The separate constitutive

modeling of the white matter and gray matter will be considered once the separate geometric

modeling between them is accomplished. And the future finite element head model would be

validated against more cadaveric head experiments.

In sum, the understanding of cerebral mechanical responses to the blasts in the various

cases along with the injury predictions of contusion and subdural hemorrhage in the present

study were essential for improving the medical care of bTBI and for developing the next-

generation protective gear to better protect people from blasts.

124

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